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This new and revised edition contains at the end of the volume 
answers to the problems in the text calculated for the year of 1921, 



SIMPLE RULES 

AND 

PROBLEMS IN NAVIGATION 



BY 

CHARLES H. CUGLE 

Licensed Master Mariner 



Corrected and Revised by 
BRADLEY JONES 



SEVENTH AND REVISED EDITION 

WITH ADDENDA CONTAINING ANSWERS TO THE NAVIGATION 
PROBLEMS FOR THE YEARS 1920 AND 1921 




NEW YORK 
E. P. DUTTON & COMPANY 

681 Fifth Avenue 



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Copyright, 1919 
Bt E. p. button & COMPANY 



All Rights Reserved 



Sixth Printing . ' . May, 1920 
Seventh Printing, September, 1920 



Printtd in tht United States of Amerieot 

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TO 

illr- ?|enrp ?|atDarb 

FORMERLY DIRECTOR OF RECRUITING SERVICE 
UNITED STATES SHIPPING BOARD 

As a mark of appreciation of the Service rendered by him in 
replacing the American Flag to its proper place upon the Seven 
Seas, this work is respectfully dedicated. 

The Author also wishes to extend his thanks to 

Captain Robert J. McBride 

FOBMERLT UNITED STATES LOCAL INSPECTOR OF HULLS 

New Orleans, La. 

Captain Ernest E. B, Drake 

fobmeblt atlantic coast supervisor of recruiting service 

united states shipping board 

Mr. Bradlet Jones 

instructor op navigation 

united states shipping board school 

Jersey City, N. J. 

Mr. Walton B. Smith 

formerly instructor of navigation 

united states shipping board school 

New Orleans, La. 

For their kind co-operation in compiling the information 
contained herein. 



I 



PREFACE TO THIRD EDITION 



In this edition the problems have been worked to a finer 
degree of accuracy than before. The interpolations used 
are sufficient to satisfy the strictest local inspector or the 
most rigid sea practice. 

While it is true that all positions obtained at sea, are 
subject to slight error; to the necessary observational errors 
there should not be added errors due to not using the tables 
to the limit of their accuracy. 

Bradley Jones. 



PREFACE TO SEVENTH AND REVISED EDITION 



The purpose of this book is to lay before the student all 
the rules and problems of navigation used in everyday work 
at sea, with short definitions of the theory of navigation, 
and other useful information that the young officer should 
know. 

In making up the rules for working the problems, the 
author may have repeated himself several times, but it 
has been his experience in teaching navigation that this 
is necessary to make the student understand. 

All of the various problems are worked out in full, with 
no attempt to save figures or cut down the working in any 
way. It is recommended to the beginner that he names 
everything as he goes along in his problems, as it will help 
to memorize. 

In addition to all the problems of the First Edition, 
there are examples for practice with their answers, and the 
abstract from the American Nautical Almanac for the year 
1919 for working the different problems. 

Several additional features have been embodied in this 
edition including '^The International Rule of the Road at 
Sea''; '^A Method of Preparing a Station Bill for Boat 
and Fire Drill"; ^^New Methods of finding latitude and 
longitude"; ^'Examples in How to Determine Distance 
from a Fixed Object by Four Point Bearings"; ^^ Examples 
in How to Determine Speed of Ship by Propeller Revolu- 
tions"; ^ ^Examples in How to Determine Percentage of Slip 
of Propeller"; and ^^The latest Rules (adopted in April, 
1920) of the Steamboat-Inspection Service giving the require- 
ments necessary to secure a license as Master or Mate on 
Ocean or Coastwise Steam and Sail Vessels." 

vii 



viii PREFACE TO SEVENTH AND REVISED EDITION 

Also included in the Addenda are the Answers to the 
various problems for the years 1920 and 1921. This allows 
the student to not only work the problems contained by 
using the Nautical Almanac for 1919 which is bound in 
the book, but also enables him to find the answers for the 
current year with the help of that year's Almanac. It is 
the intention of the publishers and myself to keep this 
book up to date, and by adding these different features from 
time to time to greatly enhance its value to the purchaser. 

This places the entire subject of navigation under one 
cover, and the author believes it to be the most easily 
understood one published. 

There are many excellent books on the theory of navi- 
gation, but very few that the ordinary man can under- 
stand, and this book has been published with theory 
eliminated entirely. 

One of the greatest faults with navigators of to-day is 
their tendency to try and cut down figures in their problems. 
There is no excuse for this, as a man at sea has plenty of 
time to work his problems, and it has been this tendency 
for rule of thumb methods that has been the loss of many a 
ship. It is time enough to learn the short methods after 
you know the proper way, and have had several years of 
practical experience. 

The books used in working the different problems are 
Bowditch's American Practical Navigator, American Line 
of Position Tables, American Azimuth Table and 1919 
American Nautical Ahnanac. 

The books of the First and Second Edition have been 
gone over carefully by several competent navigators, and 
all the examples are worked to the closest figure. 

It is hoped that this book will be a help to the reader, 
as the author has tried to make it in as plain language as 
possible. 

Charles H. Cugle. 

1632 Pine St., 
New Orleans, La. 






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CONTENTS 



CHAPTER I 

PAGE 

The International and Inland Rules of the Road . . 1 



CHAPTER II 
Useful Definitions and Information 30 

CHAPTER III 

Arithmetic of Navigation, Explanation of American Nautical 
Almanac and Tables, in Bowditch's American Practical 
Navigator 56 

CHAPTER IV 
Day's Work or Ship's Position by Dead Reckoning . . 72 

CHAPTER V 
Mercator's Sailing . . 105 

CHAPTER VI 
Middle Latitude Sailing 114 

CHAPTER VII 
Latitude by Meridian Altitude of Sun . , . . .118 

CHAPTER VIII 

Latitude by Meridian Altitude of Star and Finding Time of 

Star's Meridian Passage 133 

CHAPTER IX 

Lqngititde by Sun , , , ,138 

xi 



rii CONTENTS 

CHAPTER X 

PAOB 

Longitude by Sun to Find Noon Position • • • . 151 

CHAPTER XI 
Deviation by Azimuth of Sun 162 

CHAPTER XII 
Deviation by Amplitude of Sun 165 

CHAPTER XIII 
Latitude by Polaris (or North Star) 173 

CHAPTER XIV 

Altitude Azimuth, Longitude by Sun, Latitude by Sun and 

Mercator's Sailing Combined 178 

CHAPTER XV 
Latitude by Meridian Altitude of Planet .... 193 

CHAPTER XVI 
Latitude by Ex-Meridian Altitude of Sun . . • . 197 

CHAPTER XVII 
Longitude by Fixed Star and Planet 212 

CHAPTER XVIII 
Latitude by Meridian Altitude of Moon .... 226 

CHAPTER XIX 
Longitude by Sunrise and Sunset Observations . • . 235 

CHAPTER XX 
Phee Prime Sight for Latitude 238 

CHAPTER XXI 
Sumner's Method 240 



CONTENTS xui 

CHAPTER XXII 

PAGE 

Marcq St. Hilairb Method 244 

CHAPTER XXIII 
Finding Time of High and Low Water 257 

CHAPTER XXIV 

Examples for Practice with their Answers . , . . 270 

Chart and Explanation of Plotting one Position Line . Facing 288 

Chart and Explanation of Plotting Marcq St. Hilaire 

Method . ''289 

Chart AND Explanation OF Plotting Sumner's Method . " 290 

Extracts from American Nautical Almanac for 1919 . . 29| 

ADDENDA 

To Find the Distance Off Any Fixed Object bt a Four- 
Point Bearing 307 

Determining Speed of Ship by Pitch of Wheel and Number 

OF Revolutions per Minute 310 

Determining the Percentage of Slip op Wheel . . .312 

Abstract from General Rules and Regulations of the 
U. S. Steamboat-Inspection Service Giving the Require- 
ments Necessary for Securing License as Master or 
Mate of Ocean or Coastwise Steam and Sail Vessels . 314 

Answers to Problems for the Year 1921 . . end of volume 



SIMPLE RULES AND PROBLEMS 
IN NAVIGATION 



CHAPTER I 

THE INTERNATIONAL AND INLAND RULES 
OF THE ROAD 



2 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

INTERNATIONAL RULES 

I.— ENACTING CLAUSE, SCOPE, AND PENALTY 

Be it enacted by the Senate and House of Representatives of the 
United States of America in Congress assembled, That the following regu- 
lations for preventing collisions at sea shall be followed by all public 
and private vessels of the United States upon the high seas and in all 
waters connected therewith, navigable by seagoing vessels. 

Art. 30. Nothing in these rules shall interfere with the operation of 
a special rule, duly made by local authority, relative to the navigation of 
any harbor, river, or inland waters. 



PRELIMINARY DEFINITIONS 

In the following rules every steam vessel which is under sail and not 
under steam is to be considered a sailing vessel, and every vessel under 
steam, whether under sail or not, is to be considered a steam vessel. 

The words " steam vessel " shall include any vessel propelled by 
machinery. 

A vessel is " under way," within the meaning of these rules, when 
she is not at anchor, or made fast to the shore, or aground. 

II.— LIGHTS, AND SO FORTH 

The word " visible " in these rules when applied to lights shall mean 
visible on a dark night with a clear atmosphere. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 3 

INLAND RULES 

I._ENACTING CLAUSE, SCOPE, AND PENALTY 

Whereas the provisions of chapter eight hundred and two of the laws of 
eighteen hundred and ninety, and the amendments thereto, adopting 
regulations for preventing collisions at sea [i.e., international rules of 
left-hand column], apply to all waters of the United States con- 
nected with the high seas navigable by sea-going vessels, except 
so far as the navigation of any harbor, river, or inland waters is 
regulated by special rules duly made by local authority; and 
Whereas it is desirable that the regulations relating to the navigation 
of all harbors, rivers, and inland waters of the United States, except 
the Great Lakes and their connecting and tributary waters as far 
east as Montreal and the Red River of the North and rivers empty- 
ing into the Gulf of Mexico and their tributaries, shall be stated in 
one act: Therefore, 
Be it enacted by the Senate and House of Representatives of the 
United States of America in Congress assembled. That the following 
regulations for preventing colHsions shall be followed by all vessels navi- 
gating all harbors, rivers, and inland waters of the United States, except 
the Great Lakes and their connecting and tributary waters as far east as 
Montreal and the Red River of the North and rivers emptying into the 
Gulf of Mexico and their tributaries, and are hereby declared special rules 
duly made by local authority: 

Sec. 3. That every pilot, engineer, mate, or master of any steam 
vessel, and every master or mate of any barge or canal boat, who neglects 
or refuses to observe the provisions of this act, or the regulations estab- 
lished in pursuance of the preceding section [see section 2, page 4], shall 
be hable to a penalty of fifty dollars, and for all damages sustained by any 
passenger in his person or baggage by such neglect or refusal: Provided, 
That nothing herein shall relieve any vessel, owner, or corporation from 
any liability incurred by reason of such neglect or refusal. 

Sec. 4. That every vessel that shall be navigated without complying 
with the provisions of this act shall be liable to a penalty of two hundred 
dollars, one-half to go to the informer, for which sum the vessel so navi- 
gated shall be liable and may be seized and proceeded against by action 
in any district court of the United States having jurisdiction of the 
offense. 

PRELIMINARY DEFINITIONS 

In the following rules every steam vessel which is under sail and not 
under steam is to be considered a sailing vessel, and every vessel under 
steam whether under sail or not, is to be considered a steam vessel. 

The words " steam vessel " shall include any vessel propelled by 
machinery. 

A vessel is " under way," within the meaning of these rules, when 
she is not at anchor, or made fast to the shore, or aground. 

II.— LIGHTS, AND SO FORTH 

The word " visible " in these rules, when applied to lights, shall mean 
visible on a dark night with a clear atmosphere. 



4 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

INTERNATIONAL RULES 

Article 1. The rules concerning lights shall be complied with in all 
weathers from sunset to sunrise, and during such time no other lights which 
may be mistaken for the prescribed lights shall be exhibited. 

STEAM VESSELS — MASTHEAD LIGHT 

Art. 2. A steam vessel when under way shall carry — (a) On or in 
front of the foremast, or if a vessel without a foremast, then in the fore 
part of the vessel, at a height above the hull of not less than twenty feet, 
and if the breadth of the vessel exceeds twenty feet, then at a height above 
the hull not less than such breadth, so, however, that the Hght need not 
be carried at a greater height above the hull than forty feet, a bright 
white light, so constructed as to show an unbroken light over an arc of 
the horizon of twenty points of the compass, so fixed as to throw the light 
ten points on each side of the vessel, namely, from right ahead to two points 
abaft the beam on either side, and of such a character as to be visible at a 
distance of at least five miles. 

STEAM VESSELS — SIDE LIGHTS 

(b) On the starboard side a green light so constructed as to show an 
unbroken light over an arc of the horizon of ten points of the compass, 
so fixed as to throw the Hght from right ahead to two points abaft the beam 
on the starboard side, and of such a character as to be visible at a dis- 
tance of at least two miles. 

(c) On the port side a red light so constructed as to show an un- 
broken Hght over an arc of the horizon of ten points of the compass, so 
fixed £ts to throw the Hght from right ahead to two points abaft the beam 
on the port side, and of such a character as to be visible at a distance of 
at least two miles. 

(d) The said green and red side lights shaU be fitted with inboard 
screens projecting at least three feet forward from the light, so as to pre- 
vent these lights from being seen across the bow. 

STEAM VESSELS — RANGE LIGHTS 

(e) A steam vessel when under way may carry an additional white 
light similar in construction to the Hght mentioned in subdivision (a). 
These two Hghts shaU be so placed in line with the keel that one shall 
be at least fifteen feet higher than the other, and in such a position with 
reference to each other that the lower light shall be forward of the upper 
one. The vertical distance between these lights shall be less than the 
horizontal distanee. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION Q 

INLAND RULES 

Article 1. The rules concerning lights shall be complied with in 
all weathers from sunset to sunrise, and during such time no other lights 
which may be mistaken for the prescribed lights shall be exhibited. 

STEAM VESSELS — MASTHEAD LIGHT 

Art. 2. A steam vessel when under way shall carry — (a) On or in the 
front of the foremast, or if a vessel without a foremast, then in the fore 
part of the vessel, a bright white light so constructed as to show an 
unbroken light over an arc of the horizon of twenty points of the com- 
pass, so fixed as to throw the light ten points on each side of the vessel, 
namely, from right ahead to two points abaft the beam on either side, and 
of such a character as to be visible at a distance of at least five miles. 



STEAM VESSELS — SIDE LIGHTS 

(b) On the starboard side a green light so constructed as to show an 
unbroken light over an arc of the horizon of ten points of the compass, 
so fixed as to throw the light from right ahead to two points abaft the 
beam on the starboard side, and of such a character as to be visible at a 
distance of at least two miles. 

(c) On the port side a red light so constructed as to show an unbroken 
fight over an arc of the horizon of ten points of the compass, so fixed as 
to throw the light from right ahead to two points abaft the beam on the 
port side, and of such a character as to be visible at a distance of at least 
two miles. 

(d) The said green and red side lights shall be fitted with inboard 
screens projecting at least three feet forward from the fight, so as to pre- 
vent these lights from being seen across the bow. 

STEAM VESSELS — RANGE LIGHTS 

(e) A seagoing steam vessel when under way may carry an additional 
white light similar in construction to the light mentioned in subdivision (a). 
These two lights shall be so placed in line with the keel that one shall be 
at least fifteen feet higher than the other, and in such a position with refer- 
ence to each other that the lower light shaU be forward of the upper one. 
The vertical distance between these fights shall be less than the horizontal 
distance. 

(f) AU steam vessels (except seagoing vessels and ferryboats), shall 
carry in addition to green and red lights required by article two (b), (c), 
and screens as required by article two (d), a central range of two white 
fights; the after light being carried at an elevation at least fifteen feet 
above the light at the head of the vessel. The headlight shall be so con- 
structed as to show an unbroken light through twenty points of the com- 
pass, namely, from right ahead to two points abaft the beam on either side 
of the vessel, and the after light so as to show all around the horizon. 



6 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

INTERNATIONAL RULES 

STEAM VESSELS WHEN TOWING 

Aet 3. A steam vessel when towing another vessel shall, in addition 
to her side lights, carry two bright white lights in a vertical line one over 
the other, not less than six feet apart, and when towing more than one 
vessel shall carry an additional bright white hght six feet above or below 
such lights, if the length of the tow measuring from the stern of the towing 
vessel to the stern of the last vessel towed exceeds six hundred feet. 
Each of these lights shall be of the same construction and character, and 
shall be carried in the same position as the white light mentioned in 
article two (a), excepting the additional light, which may be carried at a 
height of not less than fourteen feet above the hull. 

Such steam vessel may carry a small white light abaft the funnel or 
aftermast for the vessel towed to steer by, but such light shall not be 
visible forward of the beam. 

SPECIAL LIGHTS 

Art. 4. (a) A vessel which from any accident is not under command 
shall carry at the same height as a white light mentioned in article two 
(a), where they can best be seen, and if a steam vessel in lieu of that 
light two red lights, in a vertical line one over the other, not less than six 
feet apart, and of such a character as to be visible all around the horizon 
at a distance of at least two miles; and shall by day carry in a vertical 
line one over the other, not less than six feet apart, where they can best 
be seen, two black balls or shapes, each two feet in diameter. 

(b) A vessel employed in laying or in picking up a telegraph cable 
shall carry in the same position as the white light mentioned in article 
two (a), and if a steam vessel in lieu of that light three lights in a vertical 
line one over the other not less than six feet apart. The highest and low- 
est of these lights shall be red, and the middle hght shall be white, and they 
shall be of such a character as to be visible all around the horizon, at a 
distance of at least two miles. By day she shall carry in a vertical hne, 
one over the other, not less than six feet apart, where they can best be 
seen, three shapes not less than two feet in diameter, of which the highest 
and lowest shall be globular in shape and red in color, and the middle one 
diamond in shape and white. 

(c) The vessels referred to in this article, when not making way through 
the water, shall not carry the side lights, but when making way shall 
carry them. 

(d) The lights and shapes required to be shown by this article are to 
be taken by other vessels as signals that the vessel showing them is not 
under command and can not therefore get out of the way. 

These signals are not signals of vessels in distress and requiring assist- 
ance. Such signals are contained in article thirty-one. 

LIGHTS FOR SAILING VESSELS AND VESSELS IN TOW 

Art. 5. A sailing vessel under way and any vessel being towed shall 
carry the same Ughts as are prescribed by article two for a steam vessel 
under way, with the exception of the white hghts mentioned therein, 
which they shall never carry. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 7 

INLAND RULES 

STEAM VESSELS WHEN TOWING 

Art. 3. A steam vessel when towing another vessel shall, in addition 
to her side lights, carry two bright white hghts in a vertical line one over 
the other, not less than three feet apart, and when towing more than one 
vessel shall carry an additional bright white light three feet above or 
below such lights, if the length of the tow measuring from the stern of 
the towing vessel to the stern of the last vessel towed exceeds six hundred 
feet. Each of these lights shall be of the same construction and char- 
acter, and shall be carried in the same position as the white light mentioned 
in article two (a) or the after range light mentioned in article two (f). 

Such steam vessel may carry a small white light abaft the funnel or 
aftermast for the vessel towed to steer by, but such light shall not be 
visible forward of the beam. 



LIGHTS FOR SAILING VESSELS AND VESSELS IN TOW 

Art. 5. A sailing vessel under way or being towed shall carry the same 
lights as are prescribed by article two for a steam vessel under way, with 
the exception of the white lights mentioned therein, which they shall never 
carry. 



8 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

INTERNATIONAL RULES 



LIGHTS FOR SMALL VESSELS 

Art. 6. Whenever, as in the case of small vessels under way during 
bad weather, the green and red side lights can not be fixed, these lights 
shall be kept at hand, lighted and ready for use; and shall, on the approach 
of or to other vessels, be exhibited on their respective sides in sufficient 
time to prevent collision, in such manner as to make them most visible, 
and so that the green light shall not be seen on the port side nor the red 
light on the starboard side, nor. if practicable, more than two points 
abaft the beam on their respective sides. To make the use of these 
portable lights more certain and easy the lanterns containing them shall 
each be painted outside with the color of the light they respectively con- 
tain, and shal^^be provided with proper screens. 

LIGHTS FOR SMALL STEAM AND SAIL VESSELS AND OPEN BOATS 

Art. 7. Steam vessels of less than forty, and vessels under oars or 
sails of less than twenty tons gross tonnage, respectively, and rowing 
boats, when under way, shall not be required to carry the lights mentioned 
in article two (a), (b), and (c), but if they do not carry them they shall be 
provided with the following lights: 

First. Steam vessels of less than forty tons shall carry — 

(a) In the fore part of the vessel, or on or in front of the funnel, where 
it can best be seen, and at a height above the gunwale of not less than 
nine feet, a bright white light constructed and fixed as prescribed in article 
two (a), and of such a character as to be visible at a distance of at least 
two miles. 

(b) Green and red side lights constructed and fixed as prescribed in 
article two (b) and (c), and of such a character as to be visible at a distance 
of at least one mile, or a combined lantern showing a green light and a 
red light from right ahead to two points abaft the beam on their respective 
sides. Such lanterns shall be carried not less than three feet below the 
white light. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 9 

INLAND RULES 

LIGHTS FOR FERRYBOATS, BARGES, AND CANAL BOATS IN TOW 

Sec. 2. That the supervismg inspectors of steam vessels and the 
Supervising Inspector-General shall establish such rules to be observed 
by steam vessels in passing each other and as to the lights to be carried 
by ferryboats and by barges and canal boats when in tow of steam vessels 
(and as to the lights and day signals to be carried by vessels, dredges of 
all types, and vessels working on wrecks by [or] other obstruction to 
navigation or moored for submarine operations, or made fast to a sunken 
object which may drift with the tide or be towed) not inconsistent with the 
provisions of this act, as they from time to time may deem necessary 
for safety, which rules when approved by the Secretary of Commerce 
are hereby declared special rules duly made by local authority, as provided 
for in article thirty of chapter eight hundred and two of the laws of eigh- 
teen hundred and ninety. Two printed copies of such rules shall be 
furnished to such ferryboats (barges, dredges, canal boats, vessels working 
on wrecks) and steam vessels, which rules shall be kept posted up in con- 
spicuous places in such vessels (barges, dredges, and boats). 

LIGHTS FOR SMALL VESSELS 

Art. 6. Whenever, as in the case of vessels of less than ten gross tons 
under way during bad weather, the green and red side hghts can not be 
fixed, these lights shall be kept at hand, lighted and ready for use; and 
shall, on the approach of or to other vessels, be exhibited on their re- 
spective sides in sufficient time to prevent collision, in such manner as to 
make them most visible, and so that the green light shall not be seen on the 
port side nor the red light on the starboard side, nor, if practicable, more 
than two points abaft the beam on their respective sides. To make the 
use of these portable lights more certain and easy the lanterns containing 
them shall each be painted outside with the color of the light they respec- 
tively contain, and shall be provided with proper screens. 



Art. 7. Rowing boats whether under oars or sail, shall have ready 
at hand a lantern showing a white light which shall be temporarily ex- 
hibited in sufficient time to prevent collision. 



10 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

INTERNATIONAL RULES 

Second. Small steamboats, such as are carried by seagoing vessels, 
may carry the white light at a less height than nine feet above the gunwale, 
but it shall be carried above the combined lantern mentioned in sub- 
division one (b). 

Third. Vessels under oars or sails of less than twenty tons shall have 
ready at hand a lantern with a green glass on one side and a red glass on 
the other, which, on the approach of or to other vessels, shall be exhibited 
in sufficient time to prevent coUision so that the green light shall not be 
seen on the port side nor the red light on the starboard side. 

. Fourth. Rowing boats, whether under oars or sail, shall have ready 
at hand a lantern showing a white light which shall be temporarily ex- 
hibited in sufficient time to prevent collision. 

The vessels referred to in this article shall not be obliged to carry the 
lights prescribed by article four (a) and article eleven, last paragraph. 

LIGHTS FOR PILOT VESSELS 

Art. 8. Pilot vessels when engaged on their station on pilotage duty 
shall not show the lights required for other vessels, but shall carry a white 
light at the masthead, visible all around the horizon, and shall also exhibit 
a flare-up light or flare-up Hghts at short intervals, which shall never 
exceed fifteen minutes. 

On the near approach of or to other vessels they shall have their side 
lights lighted, ready for use, and shall flash or show them at short intervals, 
to indicate the direction in which they are heading, but the green light 
shall not be shown on the port side, nor the red Ught on the starboard side. 

A pilot vessel of such a class as to be obliged to go alongside of a vessel 
to put a pilot on board may show the white light instead of carrying it 
at the masthead, and may, instead of the colored hghts above mentioned, 
have at hand, ready for use, a lantern with green glass on the one side 
and red glass on the other, to be used as prescribed above. 

Pilot vessels when not engaged on their station on pilotage duty shall 
carry lights similar to those of other vessels of their tonnage. 

A steam pilot vessel, when engaged on her station on pilotage duty 
and in waters of the United States, and not at anchor, shaU, in addition 
to the lights required for all pilot boats, carry at a distance of eight feet 
below her white masthead light a red Ught, visible all around the horizon 
and of such a character as to be visible on a dark night with a clear atmo- 
sphere at a distance of at least two miles, and also the colored side lights 
required to be carried by vessels when under way. 

When engaged on her station on pilotage duty and in waters of the 
United States, and at anchor, she shall carry in addition to the hghts 
required for all pilot boats the red light above mentioned, but not the 
colored side lights. When not engaged on her station on pilotage duty, 
she shall carry the same lights as other steam vessels. 



LIGHTS, ETC., OF FISHING VESSELS 

Art. 9. Fishing vessels and fishing boats, when under way and when 
not required by this article to carry or show the hghts hereinafter specified, 
shall carry or show the Hghts prescribed for vessels of their tonnage 
under way. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 11 
INLAND RULES 



LIGHTS FOR PILOT VESSELS 

Art. 8. Pilot vessels when engaged on their stations on pilotage duty- 
shall not show the lights required for other vessels, but shall carry a white 
light at the masthead, visible all around the horizon, and shall also exhibit 
a flare-up light or flare-up lights at short intervals, which shall never 
exceed fifteen minutes. 

On the near approach of or to other vessels they shall have their 
side lights lighted, ready for use, and shall flash or show them at short 
intervals, to indicate the direction in which they are heading, but the 
green Hght shall not be shown on the port side nor the red light on the star- 
board side. 

A pilot vessel of such a class as to be obliged to go alongside of a 
vessel to put a pilot on board may show the white light instead of carry- 
ing it at the masthead, and may, instead of the colored lights above 
mentioned, have at hand, ready for use, a lantern with a green glass on the 
one side and a red glass on the other, to be used as prescribed above. 

Pilot vessels, when not engaged on their station on pilotage duty, 
shall carry lights similar to those of other vessels of their tonnage. 

A steam pilot vessel, when engaged on her station on pilotage duty 
and in waters of the United States, and not at anchor, shall, in addition 
to the lights required for all pilot boats, carry at a distance of eight feet 
below her white masthead light a red light, visible all around the horizon 
and of such a character as to be visible on a dark night with a clear atmo- 
sphere at a distance of at least two miles, and also the colored side lights 
required to be carried by vessels when under way. 

When engaged on her station on pilotage duty and in waters of the 
United States, and at anchor, she shall carry in addition to the lights 
required for all pilot boats the red light above mentioned, but not the 
colored side Hghts. When not engaged on her station on pilotage duty, 
she shall carry the same hghts as other steam vessels. 

LIGHTS, ETC., OF FISHING VESSELS 

Art. 9. (a) Fishing vessels of less than ten gross tons, when under 
way and when not having their nets, trawls, dredges, or lines in the water, 
shall not be obhged to carry the colored side lights; but every such vessel 
shall, in lieu thereof, have ready at hand a lantern with a green glass on 



12 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

INTERNATIONAL RULES 

(a) Open boats, by which is to be understood boats not protected from 
the entry of sea water by means of a continuous deck, w^hen engaged in 
any fishing at night, with outlying tackle extending not more than one 
hundred and fifty feet horizontally from the boat mto the seaway, shall 
carry one all-round white Hght. 

Open boats, when fishing at night, with outljdng tackle extending more 
than one hundred and fifty feet horizontally from the boat into the sea- 
way, shall carry one all-round white light, and in addition, on approaching 
or being approached by other vessels, shall show a second white light at 
least three feet below the first light and at a horizontal distance of at least 
five feet away from it in the direction in which the outlying tackle is 
attached. 

(b) Vessels and boats, except open boats as defined in subdivision (a), 
when fishing with drift nets, shall, so long as the nets are w^holly or partly 
in the water, carry two white lights where they can best be seen. Such 
lights shall be placed so that the vertical distance between them shall be 
not less than six feet and not more than fifteen feet, and so that the hori- 
zontal distance between them, measured in a line with the keel, shall be 
not less than five feet and not more than ten feet. The lower of these 
two lights shall be in the direction of the nets, and both of them shall be 
of such a character as to show all around the horizon, and to be visible 
at a distance of not less than three miles. 

Within the Mediterranean Sea and in the seas bordering the coasts of 
Japan and Korea sailing fishing vessels of less than twenty tons gross 
tonnage shall not be obliged to carry the lower of these two Ughts. Should 
they, however, not carry it, they shall show in the same position (in the 
direction of the net or gear) a white light, visible at a distance of not less 
than one sea mile, on the approach of or to other vessels. 

(c) Vessels and boats, except open boats as defined in subdivision (a), 
when line fishing with their lines out and attached to or hauling their 
hues, and when not at anchor or stationary within the meaning of sub- 
division (h), shall carry the same lights as vessels fishing with drift nets. 
When shooting lines, or fishing with towing lines, they shall carry the 
lights prescribed for a steam or sailing vessel under way, respectively. 

Within the Mediterranean Sea and in the seas bordering the coasts of 
Japan and Korea sailing fishing vessels of less than twenty tons gross 
tonnage shall not be obliged to carry the lower of these two fights. Should 
they, however, not carry it, they shaU show in the same position (in the 
direction of the fines) a white light, visible at a distance of not less than 
one sea mile on the approach of or to other vessels. 

(d) Vessels when engaged in trawling, by which is meant the dragging 
of an apparatus along the bottom of the sea — 

First, if steam vessels, shall carry in the same position as the white 
light mentioned in article two (a) a tri-colored lantern so constructed and 
fixed as to show a white light from right ahead to two points on each bow, 
and a green fight and a red fight over an arc of the horizon from two points 
on each bow to two points abaft the beam on the starboard and port sides, 
respectively; and not less than six nor more than twelve feet below the tri- 
colored lantern a white light in a lantern, so constructed as to show a 
clear, uniform and unbroken light all around the horizon. 

Second, if sailing vessels, shall carry a white light in a lantern, so 
constructed as to show a clear, uniform, and unbroken light all around 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 13 

INLAND RULES 

one side and a red glass on the other side, and on approaching to or 
being approached by another vessel such lantern shall be exhibited in 
sufficient time to prevent collision, so that the green light shall not be 
seen on the port side nor the red light on the starboard side. 

(b) All fishing vessels and fishing boats of ten gross tons or upward, 
when under way and when not having their nets, trawls, dredges, or lines 
in the water, shall carry and show the same fights as other vessels under 
way. 

(c) AU vessels, when trawling, dredging, or fishing with any kind of 
drag nets or lines, shall exhibit from some part of the vessel where they 
can be best seen, two lights. One of these lights shall be red and the 
other shall be white. The red fight shall be above the white light, and shall 
be at a vertical distance from it of not less than six feet and not more 
than twelve feet; and the horizontal distance between them, if any, shall 
not be more than ten feet. These two lights shall be of such a character 
and contained in lanterns of such construction as to be visible ah round 
the horizon, the white light a distance of not less than three miles and the 
red light of not less than two miles. 

LIGHTS FOR RAFTS OR OTHER CRAFT NOT PROVIDED FOR 

(d) Rafts, or other water craft not herein provided for, navigating by 
hand power, horse power, or by the current of the river, shall carry one or 
more good white lights, which shall be placed in such manner as shall be 
prescribed by the Board of Supervising Inspectors of Steam Vessels. 



14 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

INTERNATIONAL RULES 

the horizon, and shall also, on the approach of or to other vessels, show 
where it can best be seen a white flare-up light or torch in sufficient time 
to prevent collision. 

All lights mentioned in subdivision (d) first and second shall be 
visible at a distance of at least two miles. 

(e) Oyster dredgers and other vessels fishing with dredge nets shall 
carry and show the same lights as trawlers. 

(f) Fishing vessels and fishing boats may at any time use a flare-up 
light in addition to the lights which they are by this article required to 
carry and show, and they may also use working lights. 

(g) Every fishing vessel and every fishing boat under one hundred 
and fifty feet in length, when at anchor, shall exhibit a white light visible 
all around the horizon at a distance of at least one mile. 

Every fishing vessel of one hundred and fifty feet in length or upward, 
when at anchor, shall exhibit a white light visible all around the horizon 
at a distance of at least one mile, and shall exhibit a second light as pro- 
vided for vessels of such length by article eleven. 

Should any such vessel, whether under one hundred and fifty feet in 
length or of one hundred and fifty feet in length or upward, be attached 
to a net or other fishing gear, she shall on the approach of other vessels 
show an additional white light at least three feet below the anchor light, 
and at a horizontal distance of at least five feet away from it in the direc- 
tion of the net or gear. 

(h) If a vessel or boat when fishing becomes stationary in consequence 
of her gear getting fast to a rock or other obstruction, she shall in daytime 
haul down the day signal required by subdivision (k) ; at night show the 
light or lights prescribed for a vessel at anchor; and during fog, mist, 
falHng snow, or heavy rain storms make the signal prescribed for a vessel 
at anchor. (See subdivision (d) and the last paragraph of article 
fifteen.) 

(i) In fog, mist, falling snow, or heavy rain storms drift-net vessels 
attached to their nets, and vessels when trawling, dredging, or fishing 
with any kind of drag net, and vessels line fishing with their lines out, 
shall, if of twenty tons gross tonnage or upward, respectively, at intervals 
of not more than one minute make a blast; if steam vessels, with the 
whistle or siren, and if saiUng vessels, with the fog-horn, each blast to 
be followed by ringing the bell. Fishing vessels and boats of less than 
twenty tons gross tonnage shall not be obliged to give the above-mentioned 
signals; but if they do not, they shall make some other efficient sound 
signal at intervals of not more than one minute. 

! (k) All vessels or boats fishing with nets or lines or trawls, when under 
way, shall in daytime indicate their occupation to an approaching vessel 
by displaying a basket or other efficient signal where it can best be seen. 
If vessels or boats at anchor have their gear out, they shall, on the approach 
of other vessels, show the same signal on the side on which those vessels 
can pass. 

The vessels required by this article to carry or show the lights herein- 
before specified shall not be obliged to carry the lights prescribed by article 
four (a) and the last paragraph of article eleven. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 15 
INLAND RULES 



16 SIMPLE RULES AND PROBLEMS IN NAVIGATION 
INTERNATIONAL RULES 

LIGHTS FOR AN OVERTAKEN VESSEL 

Art. 10. A vessel which is being overtaken by another shall show 
from her stern to such last-mentioned vessel a white light or a flare-up 
light. 

The white light required to be shown by this article may be fixed 
and carried in a lantern, but in such case the lantern shall be so con- 
structed, fitted, and screened that it shall throw an unbroken light over 
an arc of the horizon of twelve points of the compass, namely, for six 
points from right aft on each side of the vessel, so as to be visible at a dis- 
tance of at least one mile. Such light shall be carried as nearly as practi- 
cable on the same level as the side lights. 

ANCHOR LIGHTS 

Art. 11. A vessel under one hundred and fifty feet in length when 
at anchor shall carry forward, where it can best be seen, but at a height 
not exceeding twenty feet above the hull, a white light, in a lantern so 
constructed as to show a clear, uniform, and unbroken light visible all 
around the horizon at a distance of at least one mile. 

A vessel of one hundred and fifty feet or upwards in length when at 
anchor shall carry in the forward part of the vessel, at a height of not less 
than twenty and not exceeding forty feet above the hull, one such light, 
and at or near the stern of the vessel, and at such a height that it shall be 
not less then fifteen feet lower than the forward light, another such 
light. 

The length of a vessel shall be deemed to be the length appearing in 
her certificate of registry. 

A vessel aground in or near a fairway shall carry the above light or 
lights and the two red lights prescribed by article four (a). 

SPECIAL SIGNALS 

Art. 12. Every vessel may, if necessary, in order to attract attention, 
in addition to the fights which she is by these rules required to carry, 
show a flare-up light or use any detonating signal that can not be mistaken 
for a distress signal. 

NAVAL LIGHTS AND RECOGNITION SIGNALS 

Art. 13. Nothing in these rules shaU interfere with the operation of 
any special rules made by the Government of any nation with respect to 
additional station and signal lights for two or more ships of war or for 
vessels sailing under convoy, or with the exhibition of recognition sig- 
nals adopted by shipowners, which have been authorized by their respec- 
tive Governments and duly registered and published. 

STEAM VESSEL UNDER SAIL BY DAY 

Art. 14. A steam vessel proceeding under sail only, but having her 
funnel up, shall carry in daytime, forward, where it can best be seen, one 
black ball or shape two feet in diameter. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 17 
INLAND RULES 

LIGHTS FOR AN OVERTAKEN VESSEL 

Art. 10. A vessel which is being overtaken by another, except a 
steam vessel with an after range light showing all around the horizon, 
shall show from her stern to such last-mentioned vessel a white light or a 
flare-up light. 



ANCHOR LIGHTS 

Art. 11. A vessel under one hundred and fifty feet in length when at 
anchor shall carry forward, where it can best be seen, but at a height not 
exceeding twenty feet above the hull, a white light, in a lantern so con- 
structed as to show a clear, uniform, and unbroken light visible all around 
the horizon at a distance of at least one mile. 

A vessel of one hundred and fifty feet or upwards in length when at 
anchor shall carry in the forward part of the vessel, at a height of not less 
than twenty and not exceeding forty feet above the hull, one such light, 
and at or near the stern of the vessel, and at such a height that it shall 
be not less than fifteen feet lower than the forward fight, another such 
fight. 

The length of a vessel shaU be deemed to be the length appearing 
in her certificate of registry. 



SPECIAL SIGNALS 

Art. 12. Every vessel may, if necessary, in order to attract attention, 
in addition to the lights which she is by these rules required to carry 
show a flare-up light or use any detonating signal that can not be mis- 
taken for a distress signal, 

NAVAL LIGHTS AND RECOGNITION SIGNALS 

Art. 13. Nothing in these rules shall interfere with the operation 
of any special rules made by the Government of any nation with respect 
to additional station and signal lights for two or more ships of war or for 
vessels sailing under convoy, or with the exhibition of recognition signals 
adopted by shipowners, which have been authorized by their respective 
Governments, and duly registered and published. 

STEAM VESSEL UNDER SAIL BY DAY. 

Art. 14. A steam vessel proceeding under sail only, but having her 
funnel up, may carry in daytime, forward, where it can best be seen, 
one black baU or shape two feet in diameter. 



18 SIMPLE RULES AND PROBLEMS IN NAVIGATION 
INTERNATIONAL RULES 
III. SOUND SIGNALS FOR FOG, AND SO FORTH 

PRELIMINARY 

Art. 15. — All signals prescribed by this article for vessels under way 
shall be given: 

First. By " steam vessels " on the whistle or siren. 

Second. By " sailing vessels " and " vessels towed " on the fog 
horn. 

The words " prolonged blast " used in this article shall mean a blast 
of from four to six seconds duration. 

A steam vessel shall be provided with an efficient whistle or siren, 
sounded by steam or by some substitute for steam, so placed that the sound 
may not be intercepted by any obstruction, and with an efficient fog 
horn, to be sounded by mechanical means, and also with an efficient bell. 
In all cases where the rules require a bell to be used a drum may be sub- 
stituted on board Turkish vessels, or a gong where such articles are used on 
board small seagoing vessels. A sailing vessel of twenty tons gross ton- 
nage or upward shall be provided with a similar fog horn and bell. 

In a fog, mist, falling snow, or heavy rain storms, whether by day or 
night, the signals described in this article shall be used as follows, namely: 

STEAM VESSEL UNDER WAY 

(a) A steam vessel having way upon her shall sound, at intervals 
of not more than two minutes, a prolonged blast. 

(b) A steam vessel under way, but stopped, and having no way 
upon her, shall sound, at intervals of not more than two minutes, two 
prolonged blasts, with an interval of about one second between. 

SAIL VESSEL UNDER WAY 

(c) A sailing vessel under way shall sound, at intervals of not more 
than one minute, when on the starboard tack, one blast; when on the 
port tack, two blasts in succession, and when with the wind abaft the beam, 
three blasts in succession. 

VESSELS AT ANCHOR OR NOT UNDER WAY 

(d) A vessel when at anchor shall, at intervals of not more than 
one minute, ring the bell rapidly for about five seconds. 

VESSELS TOWING OR TOWED 

(e) A vessel when towing, a vessel employed in laying or in picking 
up a telegraph cable, and a vessel under way, which is unable to get out 
of the way of an approaching vessel through being not under command, 
or unable to maneuver as required by the rules, shall, instead of the 
signals prescribed in subdivisions (a) and (c) of this article, at intervals 
of not more than two minutes, sound three blasts in succession, namely: 
One prolonged blast followed by two short blasts. A vessel towed may 
give this signal and she shall not give any other. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 19 

INLAND RULES 
III. SOUND SIGNALS FOR FOG, AND SO FORTH 

PRELIMINARY 

Art. 15. All signals prescribed by this article for vessels under way 
shaU be given: 

1. By *' steam vessels " on the whistle or siren. 

2. By '' sailing vessels " and " vessel towed " on the fog horn. 

The words " prolonged blast " used in this article shall mean a blast 
of from four to six seconds duration. 

A steam vessel shall be provided with an efficient whistle or siren, 
sounded by steam or by some substitute for steam, so placed that the 
sound may not be intercepted by any obstruction, and with an efficient 
fog horn; also with an efficient bell. A sailing vessel of twenty tons 
gross tonnage or upward shall be provided with a similar fog horn and 
bell. 



In fog, mist, faUing snow, or heavy rain storms, whether by day or 
night, the signals described in this article shall be used as follows, namely: 

STEAM VESSEL UNDER WAY 

(a) A steam vessel under way shall sound, at intervals of not more 
than one minute, a prolonged blast. 



SAIL VESSELS UNDER WAY 

(c) A sailing vessel under way shall sound, at intervals of not more 
than one minute, when on the starboard tack, one blast; when on the 
port tack, two blasts in succession, and when with the wind abaft the beam, 
three blasts in succession. 

VESSELS AT ANCHOR OR NOT UNDER WAY 

(d) A vessel when at anchor shall, at intervals of not more than one 
minute, ring the bell rapidly for about five seconds. 

VESSELS TOWING OR TOWED 

(e) A steam vessel when towing, shall, instead of the signals pre- 
scribed in subdivision (a) of this article, at intervals of not more than one 
minute, sound three blasts in succession, namely, one prolonged blast 
followed by two short blasts. A vessel towed may give this signal and 
she shall not give any other. 



20 SIMPLE RULES AND PROBLEMS IN NAVIGATION 
INTERNATIONAL RULES 

SMALL SAILING VESSELS AND BOATS 

Sailing vessels and boats of less than twenty tons gross tonnage 
shall not be obliged to give the above-mentioned signals, but, if they do 
not, they shall make some other efficient sound signal at intervals of not 
more than one minute. 

SPEED IN FOG 

Art. 16. Every vessel shall, in a fog, mist, falling snow, or heavy 
rain storms, go at a moderate speed, having careful regard to the existing 
circumstances and conditions. 

A steam vessel hearing, apparently forward of her beam, the fog signal 
of a vessel the position of which is not ascertained shall, so far as the cir- 
cumstances of the case admit, stop her engines, and then navigate with 
caution until danger of coUision is over. 

IV. STEERING AND SAILING RULES 

PRELIMINARY 

Risk of collision can, when circumstances permit, be ascertained by 
carefully watching the compass bearing of an approaching vessel. If the 
bearing does not appreciably change, such risk should be deemed to 
exist. 

SAILING VESSELS 

Art. 17. When two sailing vessels are approaching one another, 
so as to involve risk of collision, one of them shall keep out of the way 
of the other, as follows, namely: 

(a) A vessel which is running free shall keep out of the way of a vessel 
which is closehauled. 

(b) A vessel which is closehauled on the port tack shall keep out of 
the way of a vessel which is closehauled on the starboard tack. 

(c) When both are running free, with the wind on different sides, the 
vessel which has the wind on the port side shall keep out of the way of 
the other. 

(d) When both are running free, with the wind on the same side, the 
vessel which is to the windward shall keep out of the way of the vessel 
which is to the leeward. 

(e) A vessel which has the wind aft shall keep out of the way of the 
other vessel. 

STEAM VESSELS 

Art. 18. When two steam vessels are meeting end on, or nearly end 
on, so as to involve risk of collision, each shall alter her course to star- 
board, so that each may pass on the port side of the other. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 21 
INLAND RULES 

RAFTS, OR OTHER CRAFT NOT PROVIDED FOR 

(f) All rafts or other water craft, not herein provided for, navigating 
by hand power, horse power, or by the current of the river, shall sound a 
blast of the fog horn, or equivalent signal, at intervals of not more than 
one minute. 

SPEED IN FOG 

Art. 16. Every vessel shall, in a fog, mist, falling snow, or heavy 
rain storms, go at a moderate speed, having careful regard to the existing 
circumstances and conditions. 

A steam vessel hearing, apparently forward of her beam, the fog signal 
of a vessel the position of which is not ascertained shall, so far as the cir- 
cumstances of the case admit, stop her engines, and then navigate with 
caution until danger of colhsion is over. 

IV.— STEERING AND SAILING RULES 

PRELIMINARY 

Risk of collision can, when circumstances permit, be ascertained by 
carefully watching the compass bearing of an approaching vessel If the 
bearing does not appreciably change ; such risk should be deemed to exist. 

SAILING VESSELS 

Art. 17. When two sailing vessels are approaching one another, so 
as to involve risk of collision, one of them shall keep out of the way of the 
other as follows, namely: 

(a) A vessel which is running free shall keep out of the way of a vessel 
which is closehauled. 

(b) A vessel which is closehauled on the port tack shall keep out of 
the way of a vessel which is closehauled on the starboard tack. 

(c) When both are running free, with the wind on different sides, the 
vessel which has the wind on the port side shall keep out of the way of 
the other. 

(d) When both are running free, with the wind on the same side, the 
vessel which is to the windward shall keep out of the way of the vessel 
which is to the leeward. 

(e) A vessel which has the wind aft shall keep out of the way of the 
other vessel. 

STEAM VESSELS 

Art. 18. Rule I. When steam vessels are approaching each other 
head and head, that is, end on, or nearly so, it shall be the duty of each 
to pass on the port side of the other; and either vessel shall give, as a signal 
of her intention, one short and distinct blast of her whistle, which the 
other vessel shall answer promptly by a similar blast of her whistle, and 
thereupon such vessels shall pass on the port side of each other. But if 
the courses of such vessels are so far on the starboard of each other as 
not to be considered as meeting head and head, either vessel shall immedi- 



22 SIMPLE RULES AND PROBLEMS IN NAVIGATION 
INTERNATIONAL RULES 



This article only applies to cases where vessels are meeting end on, 
or nearly end on, in such a manner as to involve risk of collision, and does 
not apply to two vessels which must, if both keep on their respective 
courses, pass clear of each other. 

The only cases to which it does apply are when each of the two vessels 
is end on, or nearly end on to the other; in other words, to cases in which, 
by day, each vessel sees the masts of the other in a Ime, or nearly in a line, 
with her own; and by night, to cases in which each vessel is in such a 
position as to see both the side-lights of the other. 

It does not apply by day to cases in which a vessel sees another ahead 
crossing her own course; or by night, to cases where the red light of one 
vessel is opposed to the red light of the other, or where the green light of 
one vessel is opposed to the green light of the other, or where a red light 
without a green light, or a green light without a red light, is seen ahead, 
or where both green and red lights are seen anywhere but ahead. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 23 

INLAND RULES 

ately give two short and distinct blasts of her whistle, which the other ves- 
sel shall answer promptly by two similar blasts of her whistle, and they 
shall pass on the starboard side of each other. 

The foregoing only applies to cases where vessels are meeting end on, 
or nearly end on, in such a manner as to involve risk of collision; in other 
words, to cases in which, by day, each vessel sees the masts of the other 
in a line, or nearly in a line, with her own, and by night to cases in which 
each vessel is in such a position as to see both the sideUghts of the other. 



It does not apply by day to cases in which a vessel sees another ahead 
crossing her own course, or by night to cases where the red light of one 
vessel is opposed to the red hght of the other, or where the green light of 
one vessel is opposed to the green light of the other, or where a red light 
without a green light or a green light without a red light, is seen ahead, 
or where both green and red hghts are seen anywhere but ahead. 

Rule III. If, when steam vessels are approaching each other, either 
vessel fails to understand the course or intention of the other, from any 
cause, the vessel so in doubt shall immediately signify the same by giving 
several short and rapid blasts, not less than four, of the steam whistle. 

Rule V. Whenever a steam vessel is nearing a short bend or curve 
in the channel, where, from the height of the banks or other cause, a steam 
vessel approaching from the opposite direction can not be seen for a dis- 
tance of half a mile, such steam vessel, when she shall have arrived within 
half a mile of such curve or bend, shall give a signal by one long blast 
of the steam whistle, which signal shall be answered by a similar blast 
given by any approaching steam vessel that may be within hearing. 
Should such signal be so answered by a steam vessel upon the farther side 
of such bend, then the usual signals for meeting and passing shall immedi- 
ately be given and answered; but, if the first alarm signal of such vessel 
be not answered, she is to consider the channel clear and govern herself 
accordingly. 

When steam vessels are moved from their docks or berths, and other 
boats are liable to pass from any direction toward them, they shall give 
the same signal as in the case of vessels meeting at a bend, but imme- 
diately after clearing the berths so as to be fuUy in sight they shall be gov- 
erned by the steering and sailing rules. 

Rule VIII. When steam vessels are running in the same direction, 
and the vessel which is astern shall desire to pass on the right or starboard 
hand of the vessel ahead, she shall give one short blast of the steam whistle, 
as a signal of such desire, and if the vessel ahead answers with one blast, 
she shall put her helm to port; or if she shall desire to pass on the left 
or port side of the vessel ahead, she shall give two short blasts of the 
steam whistle as a signal of such desire, and if the vessel ahead answers 
with two blasts, shall put her helm to starboard; or if the vessel ahead 
does not think it safe for the vessel astern to attempt to pass at that point, 
she shall immediately signify the same by giving several short and rapid 
blasts of the steam whistle, not less than four, and under no circumstances 
shall the vessel astern attempt to pass the vessel ahead until such time 
as they have reached a point where it can be safely done, when said vessel 



24 SIMPLE RULES AND PROBLEMS IN NAVIGATION 
INTERNATIONAL RULES 



TWO STEAM VESSELS CROSSING 

Art. 19. When two steam vessels are crossing, so as to involve 
risk of collision, the vessel which has the other on her own starboard 
side shall keep out of the way of the other. 

STEAM VESSEL SHALL KEEP OUT OF THE WAY OF SAILING VESSEL 

Art. 20. When a steam vessel and a sailing vessel are proceeding in 
such directions as to involve risk of collision, the steam vessel shall keep 
out of the way of the saihng vessel. 

COURSE AND SPEED 

Art. 21. Where, by any of these rules, one of two vessels is to keep 
out of the way the other shall keep her course and speed. 

Note — When, in consequence of thick weather or other causes, such 
vessel finds herself so close that collision can not be avoided by the action 
of the giving-way vessel alone, she also shall take such action as will best 
aid to avert collision. [See articles twenty-seven and twenty-nine.] 

CROSSING AHEAD 

Art. 22. Every vessel which is directed by these rules to keep out 
of the way of another vessel shall, if the circumstances of the case admit, 
avoid crossing ahead of the other. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 25 

INLAND RULES 

ahead shall signify her willingness by blowing the proper signals. The 
vessel ahead shall in no case attempt to cross the bow or crowd upon the 
course of the passing vessel. 

Rule IX. The whistle signals provided in the rules under this article, 
for steam vessels meeting, passing, or overtaking, are never to be used 
except when steamers are in sight of each other, and the course and posi- 
tion of each can be determined in the daytime by a sight of the vessel itself, 
or by night by seeing its signal lights. In fog, mist, falling snow or heavy 
rain storms, when vessels can not see each other, fog signals only must 
be given. 

SUPPLEMENTARY REGULATIONS 

Sec. 2. That the supervising inspectors of steam vessels and the 
Supervising Inspector-General shall establish such rules to be observed 
by steam vessels in passing each other and as to the lights to be carried 
by ferryboats and by barges and canal boats when in tow of steam vessels, 
not inconsistent with the provisions of this act, as they from time to time 
may deem necessary for safety, which rules when approved by the Secre- 
tary of Commerce are hereby declared special rules duly made by local 
authority, as provided for in article thirty of chapter eight hundred and 
two of the laws of eighteen hundred and ninety. Two printed copies 
of such rules shall be furnished to such ferryboats, and steam vessels 
which rules shall be kept posted up in conspicuous places in such vessels. 

TWO steam vessels crossing 

Art. 19. When two steam vessels are crossing, so as to involve risk 
of collision, the vessel which has the other on her own starboard side shall 
keep out of the way of the other. 

STEAM vessel SHALL KEEP OUT OF THE WAY OF SAILING VESSEL 

Art. 20. When a steam vessel and a sailing vessel are proceeding 
in such directions as to involve risk of coUision, the steam vessel shall 
keep out of the way of the sailing vessel. 

s 

COURSE AND SPEED 

Art. 21. Where, by any of these rules, one of the two vessels is to 
keep out of the way, the other shall keep her course and speed. 
[See articles twenty-seven and twenty-nine.] 



CROSSING AHEAD 

Art. 22. Every vessel which is directed by these rules to keep out 
of the way of another vessel shall, if the circumstances of the case admit, 
avoid crossing ahead of the other. 



26 SIMPLE RULES AND PROBLEMS IN NAVIGATION 
INTERNATIONAL RULES 

STEAM VESSEL SHALL SLACKEN SPEED OR STOP 

Art. 23. Every steam vessel which is directed by these rules to keep 
out of the way of another vessel shall, on approaching her, if necessary, 
slacken her speed or stop or reverse. 

OVERTAKING VESSELS 

Art. 24. Notwithstanding anything contained in these rules every 
vessel, overtaking any other, shall keep out of the way of the overtaken 
vessel. 

Every vessel coming up with another vessel from any direction more 
than two points abaft her beam, that is, in such a position, with reference 
to the vessel which she is overtaking that at night she would be unable to 
see either of that vessel's side hghts, shall be deemed to be an overtaking 
vessel; and no subsequent alteration of the bearing between the two vessels 
shall make the overtaking vessel a crossing vessel within the meaning 
of these rules, or relieve her of the duty of keeping clear of the overtaken 
vessel until she is finally past and clear. 

As by day the overtaking vessel can not always know with certainty 
whether she is forward of or abaft this direction from the other vessel she 
should, if in doubt, assume that she is an overtaking vessel and keep out 
of the way. 

NARROW CHANNELS 

Art. 25. In narrow channels every steam vessel shall, when it is 
safe and practicable, keep to that side of the fairway or mid-channel which 
lies on the starboard side of such vessel. 

RIGHT OF WAY OF FISHING VESSELS 

Art. 26. Sailing vessels under way shall keep out of the way of sailing 
vessels or boats fishing with nets, or lines, or trawls. This rule shall not 
give to any vessel or boat engaged in fishing the right of obstructing a 
fairway used by vessels other than fishing vessels or boats. 

GENERAL PRUDENTIAL RULE 

Art. 27. In obeying and construing these rules due regard shall be 
had to all dangers of navigation and collision, and to any special circum- 
stances which may render a departure from the above rules necessary 
in order to avoid immediate danger. 

SOUND SIGNALS FOR PASSING STEAMERS 

Art. 28. The words " short blast " used in this article shall mean 
a blast of about one second's duration. 

When vessels are in sight of one another, a steam vessel under way, 
in taking any course authorized or required by these rules, shall indicate 
that course by the following signals on her whistle or siren, namely: 

One short blast to mean, " I am directing my course to starboard." 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 27 
INLAND RULES 

STEAM VESSEL SHALL SLACKEN SPEED OR STOP 

Art. 23. Every steam vessel which is directed by these rules to keep 
out of the way of another vessel shall, on approaching her, if necessary, 
slacken her speed or stop or reverse. 

OVERTAKING VESSELS 

Art. 24. Notwithstanding anything contained in these rules every 
vessel, overtaking any other, shall keep out of the way of the overtaken 
vessel. 

Every vessel coming up with another vessel from any direction more 
than two points abaft her beam, that is, in such a position, with reference 
to the vessel which she is overtaking that at night she v^^ould be unable to 
see either of that vessel's side lights, shall be deemed to be an overtaking 
vessel ; and no subsequent alteration of the bearing between the two ves- 
sels shall make the overtaking vessel a crossing vessel within the meaning 
of these rules, or relieve her of the duty of keeping clear of the overtaken 
vessel until she is finally past and clear. 

As by day the overtaking vessel can not always know with certainty 
whether she is forward of or abaft this direction from the other vessel she 
should, if in doubt, assume that she is an overtaking vessel and keep out 
of the way. 

NARROW CHANNELS 

Art. 25. In narrow channels every steam vessel shall, when it is 
safe and practicable, keep to that side of the fairway or mid-channel which 
lies on the starboard side of such vessel. 

RIGHT OF WAY OF FISHING VESSELS 

Art. 26. Sailing vessels under way shall keep out of the way of sail- 
ing vessels or boats fishing with nets, or lines, or trawls. This rule shall 
not give to any vessel or boat engaged in fishing the right of obstructing 
a fairway used by vessels other than fishing vessels or boats. 

GENERAL PRUDENTIAL RULE 

Art. 27. In obeying and construing these rules due regard shall be 
had to all dangers of navigation and collision, and to any special circum- 
stances which may render a departure from the above rules necessary in 
order to avoid immediate danger. 

SOUND SIGNALS FOR PASSING STEAMERS 

[See article eighteen.] 



28 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

INTERNATIONAL RULES 

Two short blasts to mean, " I am directing my course to port." 
Three short blasts to mean, " My engines are going at full speed 
astern." 



PRECAUTION 

Art. 29. Nothing in these rules shall exonerate any vessel, or the 
owner or master or crew thereof, from the consequences of. any neglect 
to carry lights or signals, or of any neglect to keep a proper lookout, or 
of the neglect of any precaution which may be required by the ordinary 
practice of seamen, or by the special circumstances of the case. 

Art. 30. [See page 2.] 



DISTRESS SIGNALS 

Art. 31. When a vessel is in distress and requires assistance from 
other vessels or from the shore the following shall be the signals to be used 
or displayed by her, either together or separately, namely: 

In the daytime — 

First. A gun or other explosive signal fired at intervals of about a 
minute. 

Second. The international code signal of distress indicated by N. C. 

Third. The distance signal, consisting of a square flag, having either 
above or below it a ball or anything resembling a ball. 

Fourth. A continuous sounding with any fog-signal apparatus. 

At night — 

First. A gun or other explosive signal fired at intervals of about 
a minute. 

Second. Flames on the vessel (as from a burning tar barrel, oil 
barrel, and so forth). 

Third. Rockets or shells throwing stars of any color or description, 
fired one at a time, at short intervals. 

Fourth. A continuous sounding with any fog-signal apparatus. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 29 

INLAND RULES 

Art. 28. When vessels are in sight of one another a steam vessel under 
way whose engines are going at full speed astern shall indicate that fact 
by three short blasts on the whistle. 

PRECAUTION 

Art. 29. Nothing in these rules shall exonerate any vessel, or the 
owner or master or crew thereof, from the consequences of any neglect 
to carry lights or signals, or of any neglect to keep a proper lookout, or 
of the neglect of any precaution which may be required by the ordinary 
practice of seamen, or by the special circumstances of the case. 

LIGHTS ON UNITED STATES NAVAL VESSELS AND REVENUE CUTTERS 

Art. 30. The exhibition of any light on board of a vessel of war of 
the United States or a Coast Guard cutter may be suspended whenever, 
in the opinion of the Secretary of the Navy, the commander in chief of a 
squadron, or the commander of a vessel acting singly, the special char- 
acter of the service may require it. 

DISTRESS SIGNALS 

Art. 31. When a vessel is in distress and requires assistance from 
other vessels or from the shore the following shall be the signals to be 
used or displayed by her, either together or separately, namely: 

In the daytime — 

A continuous sounding with any fog-signal apparatus, or firing a gun. 



At night- 



First. Flames on the vessel as from a burning tar barrel, oil barrel, 
and so forth. 

Second. A continuous sounding with any fog-signal apparatus, or 
firing a gun. 



CHAPTER II 
USEFUL DEFINITIONS AND INFORMATION 

Altitude. — The angular height of a heavenly body above 
the horizon. 

Amplitude. — The bearing (never exceeding 90°) of a 
heavenly body at rising or setting, measured from East or 
West. 

Apparent Time. — Time calculated by the sun. Yv^hen 
the sun crosses the meridian of the observer it is apparent 
noon where he is, as well as at all places on his meridian 
from pole to pole. 

Astronomical Time. — This commences at noon of the 
civil day, the hours being counted numerically from 1 to 24, 
so that the day begins and ends at noon. To convert ci^dl 
time into astronomical time proceed as follows: If the civil 
time is A. M. take 1 from the date and add 12 to the hours. 
If P. M. take away the sign P. M. and the answer will be 
Astronomical Time. 

Azimuth. — The bearing (never exceeding 180°) of a 
heavenly body calculated from the north and south points 
of the heavens. 

Chronometer. — A marine timepiece constructed with the 
idea of great accuracy, and set to the time of some first 
meridian. The Americans and English use the time of 
the meridian of Greenwich. 

Civil Time. — The civil time consists of 24 hours; it 
conunences at midnight and the first 12 hours are called 
A. M. and the second 12 hours P. M. 

Compass. — The mariner's compass consists of a mag- 
netized steel bar secured parallel to the north and south line 
of a circular card, which latter is balanced on a pivot so as 
to turn freely in the horizontal plane, and to indicate the 
magnetic meridian. The surface of the card is divided 
into 32 courses v/ith their intermediate quarters, and, in 
addition to this, all steamships have the circumference of 
the compass card graduated into degrees. 

Variation of the Compass. — The compass needle when 
uninfluenced by deviation points to the magnetic poles of 

30 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 31 

the earth, and as these do not coincide with the true or geo- 
graphical poles, the magnetic meridians form an angle with 
the true meridians, and this is called the variation of the 
compass, which varies in extent in different parts of the 
world. The magnetic North Pole is situated in Latitude 
70° North, Longitude 97° West. The magnetic South Pole 
is situated in Latitude 70° South, Longitude 145° East. 
The variation of the compass is not constant, but under- 
goes an annual change, and the amount of this yearly- 
increase or decrease will be found plainly marked on charts. 

Declination. — The angular distance of a heavenly body 
North or South of the celestial equator. 

Departure. — The amount of easting or westing made by 
a vessel in miles. 

Deviation of the Compass. — What is known as the devi- 
ation of the compass is the deflection of the compass needle 
from the magnetic meridian caused by the attraction of the 
hull, machinery, smokestacks, masts, or by certain elements 
of magnetism in the cargo. The manner of ascertaining 
the existence and amount of compass deviation is found by 
taking bearings of the sun or some fixed object. Deviation 
is named East or West according as to the North point of the 
compass is drawn to the eastward or westward of the mag- 
netic meridian. 

Equation of Time. — The difference between mean and 
apparent time. 

Latitude. — The distance of a place on the earth's surface 
north or south of the equator, expressed in degrees, min- 
utes and seconds. 

Longitude. — The distance of a place on the earth's sur- 
face east or west of some given prime meridian, expressed 
in degrees, minutes and seconds. 

Longitude in Time. — The position or distance of a vessel 
east or west of a given prime meridian, expressed in hours, 
minutes and seconds. 

Magnetic Bearing. — The direction pointed out by the 
magnetic meridian. 

Compass Bearing. — The direction pointed out by the 
compass. 

Mean Noon. — The time that the mean sun is supposed 
to cross the meridian of the observer. 

Mean Sun. — An imaginary sun which is supposed to 
move uniformly, and to cross the same meridian at the 
same time every day, thus giving a value of exactly 24 



32 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

hours to the day. This mean or fictitious sun sometimes 
crosses the observers meridian a httle in advance of the 
true sun, and other times a Httle after it, and this differ- 
ence or interval between the real and imaginary suns is 
known as the equation of time. 

Mean Time. — Time calculated by the motion of the 
mean sun. All watches and clocks represent mean time. 

Mercators Sailing. — A method of finding the true 
course and distance between two places by emplojdng 
meridional parts instead of the middle latitude. 

Meridian. — The highest point reached by a heavenly- 
body from its rising to its setting. 

Meridian Altitude. — The angular height of a heavenly 
body from the horizon line at the time the body is crossing 
the meridian. 

Middle Latitude Sailing. — The method of finding the 
true course and distance between two places by employing 
the middle latitude between them. 

Parallax. — Is the correction applied to observed altitude 
of sun, caused by observing the sun from earth's surface 
instead of center. 

Parallel Sailing. — Sailing on a parallel; sailing true east 
or west. 

Pelorus. — An instrument much used for observing 
bearings and for finding the deviation of the compass. It is 
a dummy compass with sight vanes attached. 

Polar Distance. — The angular distance of a heavenly 
body from the pole nearest the observer. 

Refraction. — The change of direction of a ray of light 
in passing through atmospheric mediums of varying density. 

Semi-diameter. — Half a diameter, or the distance from 
top or bottom of the sun to the center. 

Sextant. — An instrument of reflection used by naviga- 
tors for measuring the altitudes of heavenly bodies. 

The Sextant. — The sextant derives its name from the 
extent of its limb, which is the sixth part of a circle, or 60°, 
but being an instrument of double reflection it is divided 
into 120°. 

The Quadrant. — The quadrant is properly an Octant, as 
the limb is only the eighth part of a circle, or 45°, but, like 
the sextant, being an instrument of double reflection, it is 
divided into 90°. 

Both instruments are constructed on the same principle, 
and can be made equally accurate and perfect. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 33 

Siderial Time. — Time measured by the stars. Siderial 
time commences when the First Point of Aries is on the 
meridian, and is counted from 1 to 24 hours, when the 
same point returns to the meridian again. 

Solar Time. — Time measured by the sun. 

Variation. — The divergence of the compass needle from 
the true North due to pointing to the North magnetic instead 
of North geographic pole. 

Zenith Distance. — The angular distance of a heavenly 
body from the zenith of the observer. 

Zenith. — That point in the heavens directly overhead 
of the observer, and 90° distance from every point of the 
horizon. 

Prime Vertical. — A heavenly body is on the prime ver- 
tical when it bears true East or West, and is the best time to 
observe a sight for longitude, as an error of latitude will 
have no effect on the longitude. 

Right Ascension. — The distance in time of a heavenly 
body reckoned eastward on the equinoctial from the First 
Point of Aries. 

First Point of Aries. — That point in the heavens which the 
sun's center occupies when its declination changes from South 
to North, or when the sun crosses the line bound North. 

Mercator Chart. — The Mercator chart has a compass 
printed on it, with an arrow to represent the North point 
which is the top, the bottom South; East right. West left. 
Meridians are the lines running North and South, on the 
chart — those on the sides, are divided into degrees and min- 
utes, and are called Graduated Meridians. Parallels of 
latitude are the Unes running east and west — those at top 
and bottom are divided into degrees and minutes, and are 
called Graduated Parallels. Latitude is measured at the 
sides on the Graduated Meridians. Longitude is measured 
at the top and bottom on the Graduated Parallels. A 
Mercator chart is a distortion of the earth's surface, the 
meridians being equal, and the parallels increased from the 
equator to the poles. The outer compass is a true compass, 
and the inner compass is a magnetic compass. The varia- 
tion is found printed on the compass, and also lines of varia- 
tion will be found on chart. Soundings are given in fathoms 
in clear parts, and in feet in shaded parts, and the nature of 
bottom is given by letters abbreviated. The chart gives all 
information as to lightships, light houses, visibihty of hghts, 
and nature of lights. 



34 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

Clinometer. — An instrument used for registering amount 
of list or heel, generally to be found on the binnacle. As one 
degree of hst will frequently alter the deviation to a like 
amount, this will require careful watching. It also comes 
in handy when putting ship in dry dock to ascertain if ship 
is upright. 

Hydrometer. — An instrument used for measuring the 
density or the specific gravity of liquids, used by seamen 
for finding the different drafts that a ship will float at, in 
fresh and salt water. The specific gravity of fresh water is 
1000. The specific gravity of salt water is 1026. To find 
the draft a ship can be loaded to in fresh water, in order to 
ascertain the amount of water she will draw at sea, proceed 
as follows: Take the density of water at wharf, from below 
the surface if possible, by hydrometer. Multiply mean 
draft of ship by this reading, and divide by 1026. The 
result will be mean sea draft. (By mean sea draft is meant 
adding forward and after draft together, and dividing sum 
by 2.) For example: Dock water reading of hydrometer 
1006. Mean draft of vessel 21 ft. 

1006x21 on«^^ J r* 

— =20.6 ft. mean sea draft. 

lU^o 

Mercurial Barometer. — The barometer is an instrument 
used for determining at any moment the weight or pressure 
of the atmosphere in its immediate vicinity. It is made 
by taking a glass tube sealed at one end, and placing the 
other end in a receptacle containing merciu-y. The mer- 
cury will then descend the tube until the weight of the col- 
umn of mercury in the tube is balanced by the atmospheric 
pressure or weight on the mercury in the cup. The glass tube 
is graduated in proper ratio, so that the increase or decrease 
of pressure can be read on the scale at the side of the glass. 

Aneroid Barometer. — Is another type of barometer, 
which, owing to its compact form, and the fact that no 
liquid is used, is coming into use more and more for sea 
service. The varying pressure of the atmosphere is regis- 
tered on the dial by a hand, which is controlled by the 
expansion or contraction of a metal box, generally of a cir- 
cular form with corrugated surface, from which almost all 
air has been withdrawn leaving a partial vacuum. 

The instruments should not be removed from the ship, 
but frequent comparisons should be made to ascertain error 
of instrument by reading barometer at 12-hour intervals 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 35 

3 times (8 A. M. or Noon preferable) and forwarding same 
to Local Weather Bureau. 

To Find the Storm Center of Tropical Cyclonic Storms. — 
In the Northern Hemisphere look into wind and 8 points 
to the right will be the center. In the Southern Hemis- 
phere 8 points to the left will be center approximately. 

Notices to be Posted on Steamers Carrying Passengers. — 
Certificate of Inspection, 2 Copies of Pilot Rules, 2 Copies of 
Safety First, 3 Copies Excluding Certain Persons from Pilot 
House, 3 Copies of Station Bills required, 5 Copies of Line 
Carrying Gun Drill, Station Bills for Fire and Boat Drills 
for Deck and Engineer's Department, Life Preserver Notices 
to be posted in each stateroom and in conspicuous places 
around vessel. Also to have on board 2 Copies of Law 
Governing the Steamboat Inspection Service, and 1 Copy of 
General Rules and Regulations of the Board of Supervising 
Inspectors. 

Dangerous Articles Forbidden on Passenger Steamers. — 
No loose hay, loose cotton, or loose hemp, camphene, nitro- 
glycerine, naphtha, benzine, coal oil, crude or refined petro- 
leum, benzole, or other like explosive burning fluids, or like 
dangerous articles, shall be carried as freight or used as 
stores on any steamer carrying passengers. Gunpowder 
may be carried if the vessel is provided with a chest or safe 
composed of metal, or entirely lined or sheathed therewith, 
at a secure distance from any fire, after an examination has 
been made by the Local Inspectors of such chest or safe, and 
a license to carry gunpowder has been issued, such license 
to be kept conspicuously posted on board vessel. 

Watchmen Required on Passenger Steamers, — Every 
steamer carrying passengers during the night time shall 
keep a suitable number of watchmen in the cabins, and on 
each deck to guard against fire or other dangers, and to give 
alarm in case of accident or disaster. All steam^ers while 
navigating at night shall keep a man on the lookout for- 
ward if weather permits, or at some other suitable place. 

Reports to be Made to Local Inspectors. — The Master 
of every steamer shall make a report in writing to the Local 
Inspectors of any accident to vessel or loss of life. Notice 
shall be made in writing to Local Inspectors of number of 
passengers carried, and fire and boat drill practiced, each 
month. 

Drills to be Entered in Log Book. — Fire and boat drill 
shall be practiced once each week on passenger steamers. 



36 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

The line carrying gun shall be fired once every three months 
and such drills shall be entered in ship's log book. 

How Fire Hose Shall be Carried. — Fire hose shall be 
carried connected to fire plugs, and ready for immediate 
use, with suitable spanners at each plug. 

Lamp and Paint Locker Requirements. — All steamers 
carrying passengers shall have a metal-lined paint and lamp 
locker. This locker to have a f-in. steam pipe run into it 
for sm.othering fires, and the valve of such steam pipe shall be 
plainly marked. 

How Lifeboats shall be Carried and Marked. — All life- 
boats on steamers carrying passengers shall be carried under 
davits of approved mechanical design, capable of sustaining 
the weight of boat and equipment and number of persons 
allowed to be carried. They shall be marked in numerical 
order, odd numbers on starboard side, even numbers on port 
side, cubical contents and number of persons allowed shall 
be painted on each bow in letters not less than f in. high. 
Vessel's name and home port shall be painted on stern in 
letters 3 in. high. Number of persons allowed shall be 
painted on two thwarts in letters 3 in. high. All boats shall 
be in condition for immediate launching at all times and the 
falls shall not be painted or covered,and shall be stowed in 
covered tubs or reels on outside of boat. 

Equipment of Lifeboats. — A properly secured life line the 
entire length on each side, such fine to be festooned in bights 
not longer than 3 ft., with a seine float in each bight; at 
least 2 fife preservers; 1 painter of not less than 2 J in. 
manila rope; a full complement of oars and 2 spare oars; 
a set and a half of rowlocks, each rowlock to be attached 
to boat with a separate chain; 1 steering oar with rowlock 
or becket, or 1 rudder with yoke and suitable yoke ropes; 
1 boat hook attached to staff of a suitable length; 2 axes; 
1 bucket with lanyard attached; 1 bailer; 1 hquid compass 
with not less than 2-in. card; 1 lantern with attached 
lamp containing suflicient oil to burn at least 9 hours and 
ready for immediate use; 1 gallon of illuminating oil in a 
substantial can ; at least 1 box of friction matches wrapped 
in a waterproof package and carried in a box attached 
to the underside of the stern thwart; at least 2 quarts 
of water for each person carried, in a strong wooden 
breaker or suitable tank fitted with a siphon, pump, or 
spigot for drawing water; 2 drinking cups of enanaeled 
metal; 1 substantial metal can containing 2 lbs. of hard 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 37 

bread for each person carried, the metal bread can to be 
fitted with an opening in the top not less than 5-in. in 
diameter, properly protected with a screw cap of heavy- 
cast brass with machine thread and an attached double 
toggle seating to a pliable rubber gasket which shall 
insure a tight joint in order to properly protect the 
contents of the can; 1 canvas bag containing sailmaker^s 
palm and needles, sail twine, marline spike, and hatchet; 

12 pyrotechnic red lights carried in a metal case; 1 drag 
sail; 1 gallon of storm oil; and 1 mast and sail with neces- 
sary rigging. 

Equipment of Life Rafts. — A properly secured life line 
entirely around the sides and ends of raft festooned to the 
gunwales in bights not longer than 3 ft. with a seine float in 
each bight; 1 painter of 2f in. manila rope of a suitable 
length; 4 oars; 5 rowlocks properly attached; 1 boat hook 
attached to staff of suitable length; 1 self -igniting life-buoy 
light; 1 sea anchor; 1 vessel containing 1 gallon of vegetable 
or animal oil, so constructed that the oil can be easily dis- 
tributed on the water, and so arranged that it can be at- 
tached to the sea anchor; 2 lb. of hard bread for each person 
carried, carried in a receptacle same as in lifeboats; 1 water 
breaker containing 1 quart of water for each person carried; 
2 enameled drinking cups; 1 metal case containing 6 pyro- 
technic red lights; 1 water-tight box of matches. All loose 
equipment must be securely attached to the raft to which it 
belongs. 

How to Mark a Lead Line. — Two fathoms, 2 strips of 
leather; 3 fathoms 3 strips of leather; 5 fathoms white 
rag; 7 fathoms red rag; 10 fathoms leather with 1 hole; 

13 fathoms blue rag; 15 fathoms white rag; 17 fathoms 
red rag; 20 fathoms leather with 2 holes; 25 fathoms 
cord with 1 knot ; 30 fathoms cord with 3 knots. 

Explain the Use of the Deep Sea Sounding Machine. — 
The deep sea sounding machine has a reel of fine wire to 
which the lead is attached by a line having made fast to it 
the lead and a brass tube. Into the brass tube is placed 
the depth recorder which is a long glass tube, which is placed 
sealed end up. When the lead is armed and everything is 
ready the brake is released, and the wire is allowed to run 
out until the bottom is struck. The amount of wire run 
out is shown by an indicator on the side of the machine. 
The amount of wire is not the depth of water obtained, as 
the amount run out varies with the speed of the ship. The 



38 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

wire is then reeled back, and the glass tube is taken out. 
The pressure of the water causes the tube to become dis- 
colored a certain length up for a certain depth, and the 
amount of such depth is found by measuring the discolora- 
tion on a scale provided for that purpose. 

How to Find Course and Distance by Mercator Chart and 
Parallel Rules. — Lay the parallel rules on the two places 
that the course and distance is wanted for. After obtaining 
proper angle, move the rules to the nearest compass rose on 
the chart and read off the course obtained. Measure the 
distance between the places on the side of the chart in the 
latitude column always, using the middle latitude between 
the places. 

How to Find Ship's Position by Cross Bearings. — Take a 
bearing of two fixed objects by ship's compass, and correct 
for the deviation for ship's head and the variation at the 
place, making the bearings true. Lay off the bearings on 
the chart from the objects used, and where the two lines 
cross one another will be the ship's position at time of taking 
the bearings. 

How to Find the Distance Off a Fixed Point by Four 
Point Bearings. — Take a bearing of the object when it 
bears four points on the bow and also when abeam. If the 
ship has held the same course while taking the two bearings 
the distance run between the two bearings will be the dis- 
tance off the object when abeam. 

What is the Duty of a Mate on Watch? Keep a good 
lookout, watch the steering, see that man on lookout keeps a 
good lookout. If it comes on thick or foggy, stop or slow 
the vessel, blow the whistle, and send someone to call the 
Master. 

What Would You Do Should a Man Fall Overboard?— 
Stop the ship, throw the stern of the ship from the man, 
send a man aloft to watch out and direct the boat, throw 
over a life buoy, and lower the lee boat. 

What Would You Look After When Lowering a Boat, 
and How Would You Place Your Men in the Boat? — 
See if the plug was in the boat, and the davit falls all clear. 
Place one mian in bow and another in stern to unhook davit 
tackles, rest of crew sitting down ready with oars. 

How Would You Handle a Boat in a Heavy Surf? — I 
would head my boat to the sea and pull towards it when it 
breaks. If about to beach a boat in the surf pull in close to 
the breakers, then back the boat in, pulUng toward the sea 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 39 

as it breaks. Do not let her fall broadside too, or the boat 
will swamp. 

Your Ship is Ashore, Your Boats and Life Rafts are all 
Stove in, What Would You Do to Save the People on Board 
Your Vessel? — Send up distress rockets and make distress 
signals to attract the attention of the life-saving crew on 
shore. If not answered, build a raft out of anything that 
will float, bend a line to it, and throw the raft overboard 
and see if it will drift ashore. If so, haul it back again and 
put two good swimmers and a long hne coiled on the raft, 
and then let it drift as near the shore as it will go, then let the 
men jump over and swim ashore with the line. Then haul 
the raft backward and forward until every one is off the 
vessel. ^ 

How Would You Find the Approximate Position of a 
Vessel: by Taking One Bearing of a Point or Light? — Take 
a bearing of the point, and drop the lead. Then go to the 
chart and draw a line representing the bearing of the par- 
ticular point, and hunt along this line until the depth of 
water and natiu*e of bottom is found. The result will be 
the approximate position of the vessel. 

In Case of Collision While in Command or in Charge 
of a Watch What are your Duties? — Stop the ship and ascer- 
tain the damage to my own vessel. Call all hands to atten- 
tion, serve out hfe belts, man boats and get ready for lower- 
ing. Next ascertain if the other vessel needs assistance; 
if so, render it, if not, and both vessels are able to proceed, 
exchange names of vessels and port of registry, and imme- 
diately upon arrival in port send in a written report to the 
steamboat inspectors, and make out wreck report and file 
it at the custom house. If the report is not m.ade the Master 
is hable to a fine. 

Wliat are the Duties of a Mate Towards the Master, 
Passengers and Crew? — The duty of an officer of a vessel is 
to obey all orders emanating from his superior officer; assist 
in the navigation of the vessel to the best of his ability; 
report to the Master whenever the officer is of the opinion 
that a danger exists if the orders of his superiors are carried 
out, show an example to the crew by obeying all orders 
promptly; keep the passengers out of dangerous places; 
see that the crew know their stations in case of fire or col- 
lision ; do not molest passengers ; see that all life saving and 
fire fighting equipment is kept ready for use and in good con- 
dition; and keep a good lookout while on watch. 



40 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

What do the Figures and Letters You See on a Chart 
Represent? — The figures represent the depth of the water 
in fathoms or feet, at a mean low water, and the letters 
represent the nature of the bottom. 

If You Think You Hear a Fog Whistle on Your Bow, 
What Would You Do? — Stop my vessel, ascertain the posi- 
tion of the other vessel if possible, and then proceed with 
caution. 

How Would You Approach a Sinking Vessel With a 
Boat in a Heavy Sea and Take the People Off, if it Was Too 
Rough to go Alongside? — Run dead to windward of the 
sinking vessel as close as safety wdll permit; stop my ship 
and make one side of my ship a lee side, lower away the lee 
boat, and at the same time throw overboard a can of oil 
to smooth the sea. Let the boat drift down toward the 
wreck, and when the boat is near the wreck, look out for 
wreckage and fall in on the lee side of the wreck as near as 
possible. If dangerous to go alongside, throw the boat head 
up and let a man stand in the bow of the boat and throw a 
heaving line with a bowline in the end of it on board the 
wreck, which one of the people on board will place around 
him, and then jump overboard, and who will be hauled into 
the boat. The vessel in the meantime will run to the lee- 
ward and wait for the boat, when she leaves the wreck with 
a boat load of people. This will be repeated until every- 
body is off the wreck. 

How Would You Heave To in a Gale Under Steam, or 
With Engines Disabled? — Slow the engines, head her up 
to the sea, and get on some after canvas. If she will not 
lay to, use a drag over the weather bow. If disabled try 
to make her lay her head to the sea with a drag over her bow, 
and some after canvas, but if she would not lay to keep her 
helm amidship, take in the after canvas and pass the drag 
aft to the weather quarter and let her lay stern to. 

How Would You Approach the Land in a Fog, and Wha^ 
Precaution Would You Take? — Go slow and use the lead 
frequently. If in doubt stop and wait for weather to clear. 

When Taking Soundings, What do You Use Besides the 
Depth of Water to Confirm Your Position? — The nature of 
the bottom which is brought up on the arming of the lead. 

Buoyage System of U. S. — On entering channels nun- 
shaped or peaked buoys, red with even numbers, starboard 
side. Can-shaped or flat-top buoys, black with odd num- 
bers, port side. Black and white perpendicular striped 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 41 

buoys are fairway buoys. Black and red horizontal striped 
buoys are obstruction buoys, give berth on both sides. 
White buoys are anchorage ground, anchor inside of buoys. 
Gas, Bell and WhistHng Buoys are colored and placed accord- 
ing to the needs of surrounding and locality and are described 
in local buoy books. Buoys and beacons with cages are 
generally placed at turns in narrow channels, and may be 
colored with reference to background. 

Danger Bearing. — If crossing a vessel or approaching 
the land observe a bearing. If this bearing does not change, 
risk of collision or grounding should be assumed. 

U. S. WEATHER BUREAU SIGNALS 

The Small Craft Warning.— A red pennant displayed 
alone indicates that, while the wind may not reach a velocity 
sufficiently high to justify the display of a regular storm 
warning, they will interfere with the safe operation of small 
craft, such as those engaged in fishing, towing, motor-boat- 
ing, and yachting. 

The Storm Warning. — A red fiag (8 ft. square) with 
black center (3 ft. square) indicates that a storm of marked 
violence is expected. 

Pennants. — The pennants displayed with the flag indi- 
cates the direction from which the wind is expected to 
blow. 

The Red Pennant.— (Eight ft. hoist and 15 ft. fly) dis- 
played with the flag indicates easterly winds. 

The White Pennant.— (Eight ft. hoist and 15 ft. fly) 
displayed with the flag indicates westerly winds. 

When the red pennant is hoisted above the storm flag, 
winds are expected from the Northeast quadrant; when 
below, from the Southeast quadrant. 

When the white pennant is hoisted above the storm flag, 
winds are expected from the Northwest quadrant; when 
below, from the Southwest quadrant. 

Night Warnings. — By night, two red lights one above the 
other, indicate winds from the Northeast quadrant; a 
single red light indicates Southeast quadrant; a white fight 
above a red light indicates Northwest quadrant; and a red 
light above a white light indicates Southwest quadrant. 

The Hurricane Warning. — Two storm flags (red with 
black center), displayed one above the other, are used to 
announce the expected approach of tropical hurricanes, 



42 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

and also those extremely severe and dangerous storms 
which occasionally move across the Lakes and northern 
Atlantic Coast. 

The Night Hurricane Warning. — Two red lights with a 
white light between in a vertical line. 



INSTRUCTIONS FOR THE USE OF THE GUN AND ROCKET 
APPARATUS, AS PRACTICED BY U. S. LIFE SAVING SERVICE 

If your vessel is stranded and a shot with a small line 
is fired over it, get hold of the line, haul it on board until 
you get a tail block with an endless line rove through it, 
make the tail block fast to the lower mast well up, or in 
the event the masts have gone, to the best place to be found. 
Cast off small shot line, see that rope in block runs free, 
and make signal to shore. 

A hawser will be bent to the endless line on shore, and 
hauled off to your ship by the life-saving crew. Make 
hawser fast about 2 ft. above the tail block, and unbend 
hawser from endless line. See that rope in block runs free, 
and make signals to shore. 

Life savers on shore will then set hawser taut, and by 
means of the endless line haul off to your ship a breeches 
buoy. 

Let one man get clear into the breeches buoy, thrusting 
his legs through the breeches, make signal to shore as 
before, and he will be hauled ashore by the Hfe savers, and 
the empty buoy returned to the ship. 

The following signals have been adopted by the Coast 
Guard of the United States : 

No. 1. Upon the discovery of a wreck by night the sta- 
tion crew will burn a red pyrotechnic light or a red rocket 
to signify, " You are seen; assistance will be given as soon 
as possible." 

No. 2. A red flag waved on shore by day, or a red light, 
red rocket, or red Roman candle displayed by night, will 
signify, '' Haul away." 

No. 3. A white flag waved on shore by day, or a white 
light swung slowly back and forth, or a white rocket or 
white Roman candle fired by night, will signify, '' Slack 
away." 

No. 4. Two flags, a white and a red, waved at the same 
time on shore by day, or two fights, a white and a red, 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 43 

slowly swung at the same time, or a blue pyrotechnic light 
burned by night, will signify, '^ Do not attempt to land in 
your own boats; it is impossible/' 

No. 5. A man on shore beckoning by day, or two torches 
burning near together by night, will signify. ^' This is the 
best place to land." 

INTERNATIONAL CODE OF SIGNALS 

The International Code of Signals consists of 26 Flags — 
one for each letter of the alphabet — and a Code Flag. 

Letters '^ A " and '' B " are Burgees. 

Letters '' C," '' D," '' E," '' F " and '' G " and '' Answer- 
ing Pennant " are pennants. 

The balance of the alphabet are in square flags. 

Two Flag Signals. — Are urgent and important signals. 
Such as '^ NC " which means '' I am in distress." 

Three Flag Signals. — Are general signals. Such as 
'' CXL " which means ^' Do not abandon me." 

Four Flag Signals. — Are Geographical, Alphabetical 
Spelling Tables, and Vessels' Numbers. Such as '' AZOT " 
is the Geographical Signal for New York City. Alpha- 
betical signals are the words spelled out by the flags, and 
answered by the Answering Pennant. Vessels' Numbers 
are given in the List of Merchant Vessels. Each vessel 
having a certain number. 

Meanings of Flags and Pennants Hoisted Singly 

" B " I am taking in (or, discharging) explosives. 

" C " Yes, or. Affirmative. 

" D " No, or. Negative. 

" L " I have (or, have had) some dangerous infectious 
disease on board. 

'' P " I am about to sail; all persons to report on board. 

''Q " I have a clean bill of health, but am liable to quar- 
antine. 

'' S " I want a pilot. 

How to Make a Signal 

1. Ship A, wishing to make a signal, hoists her Ensign 
code flag under it. 

2. When Ship A has been answered by the vessel she 
is addressing she proceeds with the signal which she desires 



44 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

to make, first hauling down her code flag if it is required 
for making the signal. 

3. Each hoist should be kept flying until Ship B hoists 
her Answering Pennant. 

4. When Ship A has finished signalling she hauls down 
her Ensign. 

How to Answer a Signal 

1. Ship B (the ship signalled to) on seeing the signal 
made by Ship A, hoists her Answering Pennant at the 
" Dip.'^ 

2. When A's hoist has been taken in, looked out in the 
signal book, and is understood, B hoists her Answering 
Pennant " Close Up " and keeps it there until A hauls her 
hoist down. 

3. B then lowers her Answering Pennant to the " Dip " 
and waits for next hoist. 

4. If the flags in A's hoist cannot be made out, B keeps 
her Answering Pennant at the " Dip " and hoists the signal 
OWL or WCX, or such other signal as may meet the case; 
and when A has repeated or rectified her signal, and B 
thoroughly understands it, B hoists her Answering Pen- 
nant " Close Up." 

DOT AND DASH CODE 

This method is used to converse with vessels at sea by 
means of flashlights, flags, or whistle. 

With a little practice the reader will have no trouble in 
being proficient. 

Alphabet 

A .— N — . 

B — . . . O 

C — .— . P . . 

D — . . Q . — 

E . R .— . 

F . . — . S ... 

G . T — 

H U . .— 

I . . V .. .— 

J . W . 

K — .— X — . .— 

L . — . . Y — . 

M Z . . 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 45 

Ntimerals 



Additional Sjrmbols 

Comet Code Interval or Desig- 

Letters (follow) . nator . — . — 

Signals (follow) . . 

Conventional Signals 

End of word ' Interval 

End of sentence Double Interval 

End of message Triple Interval 

Signal separating preamble — ... — 

from address ; address from 

text; text from signatm-e 

Acknowledgment — . (R) 

Error 

Interrogatory . . 

Repeat after (word) Interrogatory, A (word) 

Repeat last word Interrogatory twice 

Repeat message Interrogatory three times 

Send faster QRQ 

Send slower : QRS 

Cease sending QRT 

Wait a moment — . . • 

Execute IX, IX 

Move to your right MR 

Move to your left ML, 

Move up MU 

Move down MD^ 

Finished (end of work) — , — 

SIMPLE RULES FOR STOWAGE OF CARGO 

When the cargo is discharged from the ship all the holds 
and ^tween decks, should be well cleaned and dunnage 
stacked up on the side ready for next cargo. 

Dunnage is loose wood, laid on the bottom and ^tween 



46 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

deck of a vessel' to prevent damage by vessel leaking, 
leaking water pipes, liquid cargo leaking, etc. 

Dunnage should be laid in the holds fore and aft about 
9 in. high, and in the 'tween deck athwartship about 3 in. 
high. The reasons for laying dunnage in this way is to 
allow any water that may get under the cargo to have 
free access to bilge suctions, and scupper pipes. 

Casks are stowed fore and aft, bung up, and bilge free, 
with dunnage under the quarters, and well chocked off. 
Begin amidship for first tier, and work towards the wings. 
To determine the location of the bung of a cask, if it is 
not visible, look for the rivets in the hoops, which will always 
be in line with the bung. 

Bale goods should be stowed on their flat, with marks 
and numbers up. 

Acids should be stowed on deck, so that it can readily 
be thrown overboard in case of leakage, and should be 
securely lashed. 

When carrying a cargo of cotton special attention should 
be given that dunnage is well laid, and all iron work in holds 
properly protected, so that no friction may occur between 
the bands of the bales and the iron work. 

A cargo of coal should be taken on board dry, and plenty 
of surface ventilation given to holds to avoid against the 
coals getting heated and taking fire. In fine weather at sea 
the hatches should be left open, and the temperature of 
the holds taken each watch. In case of fire batten down 
all hatches, ventilators, etc., and turn steam in holds, it is 
possible in some instances to hold the fire in this way. 

On taking on board a cargo of steel rails operations 
should begin in the main hold, and the iron stowed fore 
and aft until level with keelson, then stowed grating fashion. 
To protect the sides of the vessel, place rails fore and aft 
and also have locking tiers of rails; when high enough 
lash all together with chains, and place battens across 
and tom all down securely from beams; also tom from the 
sides of the vessel. 

A cargo of iron should be stowed in the body of the ves- 
sel, trimmed towards the wings, and raised up in the holds 
to a good height; by doing so the vessel will be in better 
trim for rough weather, and will not roll so heavily. 

For general cargo have all the holds cleaned and dunnage 
laid down. Consider the nature of cargo, and stow it in the 
various holds so that the vessel will be kept in good trim. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 47 

The quantity of coal in the bunkers will have to be taken 
into consideration. If the vessel is to call at a number of 
ports, the cargo should be stowed so that at the first port 
of call the cargo for that place will be handy for dis- 
charging. 

Deadweight should be stowed in the lower holds, and 
used for trimming the ship; bale goods, etc., on top; tallow 
and butter should be kept in a cool place away from fire- 
room bulkhead; liquors should be kept in a locker in the 
'tween deck for that purpose. 

A cargo of iron ore takes up little space in a vessel, as 
the ship is down to her draught before the holds are full. 
This cargo of dead weight should be placed in the body of 
the vessel, raised up in the main hold, and trimmed out 
towards the wings, also fore and aft to keep vessel in trim. 
By stowing cargo high up the vessel will behave better in 
a seaway. 

To carry a cargo of grain in bulk, have all holds cleaned 
out, and bilges clear. The holds must be divided into com- 
partments by means of fore and aft shifting boards 3 in. 
thick and athwartship bulkheads, the various compart- 
ments being grain-tight and strongly constructed from 
the bottom of the hold right up to the deck. The 'tween 
deck must be fitted with feeders to feed the lower 
hold. 

When the grain is coming on board it ought to be well 
trimmed into all the corners and tramped down, otherwise 
if the vessel encounters bad weather, she will probably take 
a heavy list by the cargo settling over to the lee side. All 
grain cargoes must be properly trimmed, stowed and 
secured. 

If the vessel is not fitted up with properly constructed 
feeders, she must have not less than one-fourth of the grain 
carried in each hold or compartment made up in bags, and 
before shipping the bags, matting and platforms must be 
laid upon the grain in bulk. 

Weights should be distributed when loading, about 
two-thirds in lower holds and one-third in 'tween deck 
approximately. 

Deck cargo should be well secured, and particular atten- 
tion given to cargo stowed on after deck to keep it clear 
from steering chains or rods. 

A practical rule for ascertaining strength of rope is given 
below : 



48 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

Square the circumference and divide by 3 for breaking 
strain in tons, by 6 for working strain. 

To find the weight rope will lift, when rove as a tackle: 

Multiply the weight the rope is capable of lifting, by the 
number of parts at the moving block, and less one-quarter 
for resistance. 

To find the number of parts of small rope required to 
equal a larger rope : 

Divide the square of the circumference of the larger rope 
by the square of the circumference of the smaller, result 
will be number of parts the smaller rope requires. 



SIMPLE RULES IN COMPASS ADJUSTMENT 

Strip compass of all magnets. Suppose the ship to be 
at sea and intended to use the sun, proceed as follows : 

Set your watch to A. T. S., take from the azimuth tables 
the sun's true bearing for every four minutes of the time 
during which you will be occupied in adjusting. Correct 
it into the correct magnetic bearing, and write it down 
plainly in a small pass book. 

Ship's Head North. — Set the lubber's point of the pelorus 
at North, and the sight vanes clamped to the sun's mag- 
netic bearing. Then starboard or port the helm until 
the sun's bearing is reflected and bisected by the thread 
of the pelorus vane. The vessel's head will now be North 
correct magnetic. If the compass agrees with the pelorus 
the compass is correct. If the compass shows easterly 
deviation, place either before or abaft a steel magnet with 
its red end to starboard above or below in the most con- 
venient place, but on the fore and aft centerline of the com- 
pass. Reverse magnets for opposite deviation. 

Ship's Head East. — Noting the A. T. S. and mag- 
netic bearing of the sun, screw lubber's Une of the pelorus 
East, and keep vanes set to the sun's correct magnetic 
bearing. Port the helm until the sun is bisected in the sight 
vanes of the pelorus, steady her carefully on this fresh 
course. If the compass agrees with the pelorus it should 
show East, should it fail to do so, the difference is the 
deviation. If westerly deviation is shown, place a steel 
magnet fore and aftways on either side of the compass 
with its red end aft, and center on the athwartship line of 
the compass. Move it slowly towards the compass until 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 49 

half of the westerly deviation is corrected. Next place 
the Flinder's bar forward of the binnacle at such a dis- 
tance as will cause the ship's head to appear due East, 
whence it may be securely bolted down to the deck. The 
semi-circular deviation of the compass is now corrected. 

Quadrantal Deviation. — Put ship's head by the pelorus 
N E (Corr Mgc), noting apparent time as before. In 
nearly every case the deviation is Easterly. Cast iron 
cylinders or globes are placed on each side of the compass 
bowl and moved near to or further from it until the ship's 
head points N E by the compass also, this adjustment 
properly made does not require touching ever after, unless 
some alterations are made in the ironwork near the com- 
pass or if the ship were to load a cargo of iron. Rule: 
The ends of the correctors must not be nearer to the center 
of the card than IJ times the length of the longest needle. 
The compass is now fully adjusted, swing the ship for final 
deviation card. 

Semi-circular deviation is so termed because it has con- 
trary names, thus if it is Easterly on North, it is Westerly 
on South. 

Quadrantal deviation is so termed because it is greatest 
on the four inter-cardinal points. It has the same name 
in opposite quadrants, thus, if it is easterly on N E, it will 
be easterly on S W also, but westerly on S E and N W. 
Thus the two kinds of deviation are vastly different. 

Steel fore and aft magnets produce their greatest effect 
on East and West, diminishing to nothing on North and 
South when they become parallel to the compass needle. 

Steel athwartship magnets produce their greatest effect 
on North and South, diminishing to nothing on East and 
West, when they become parallel to the compass needle. 

Quadrantal correctors produce their greatest effect on 
N E; S E; S W; and N W; tapering to nothing on N; S; 
E or West. 

A flinder's bar placed on the center line of the compass 
before or abaft acts in the same way as the fore and aft 
steel magnets. 



so 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 



H 




EXPLANATION BELOW WILL EXPLAIN DIAGRAM 



No. 1. The complement of an arc is 90° minus the arc. 
Thus B C is the complement of the arc A C. 

No. 2. The supplement of an arc is 180° minus the 
arc. Thus F H is the supplement of the arc A B F. 

No. 3. The sine of an arc is the perpendicular let fall 
from one extremity of the arc on the diameter which passes 
through the other extremity. Thus C D is the sine of the 
arc A C. 

No. 4. The cosine of an arc is the sine of its comple- 
ment, or it is the distance between the foot of the sine 
and center of the circle. Thus C E or D is the cosint 
of the arc A C. 

No. 5. The tangent of an arc is a line which is per- 
pendicular to the radius at one extremity of the arc and 
limited by a line passing through the center of the circle 
and the other extremity. Thus A T is the tangent of the 
arc A C. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 51 

No. 6. The cotangent of an arc is equal to the tangent 
of the complement of arc. Thus B T' is the cotangent of 
the arc A C. 

No. 7. The secant of an arc is a line drawn from the 
center of the circle through one extremity of the arc, and 
limited by a tangent at the other extremity. Thus T is 
the secant of the arc A C. 

No. 8. The cosecant of an arc is the secant of the com- 
plement of the arc. Thus T' is the cosecant of the arc 
AC. 



SHIP'S BUSINESS 

Invoice. — Is a bill of goods for stores or supplies or a 
claim against a vessel for unpaid bills, also a claim to hold 
cargo for freight unpaid. 

Bill of Lading. — A description of cargo, and an agree- 
ment to deliver same at a certain place for a certain condi- 
tion. It is made out in 3 copies, 1 for consignor, 1 for con- 
signee, and 1 for master, all signed by master. 

Manifest. — A manifest is a description of cargo, also 
of passengers if any, and their baggage, also a description 
of the vessel and its voyage. It should be signed by master 
and should be handed to boarding officer upon arrival at 
port. 

Bottomry Bond. — A bottoniry bond is where a master 
pledges his vessel as security for money loaned to complete 
voyage. 

Charter Party. — A charter party is where the master, 
owner or agent makes an agreement for the vessel to per- 
form certain services for a certain consideration. 

A Protest. — A protest should be sworn to by Master 
and members of crew before a notary, or consul if abroad. 
It is a description of some accident happening during the 
voyage, and protests against blame being placed on ship or 
crew for accident caused by the elements. 

Average. — When it is found necessary to jettison cargo, 
and some shippers cargo is sacrificed to save the rest of 
the cargo and ship, a general average is made out so that 
each should pay their proportionate part. 



52 SIMPLE RULES AND PROBLEMS IN NAVIGATION' 

METHOD OF PREPARING A STATION BILL FOR FIRE AND 
BOAT DRILL ON AN OCEAN PASSENGER STEAMER 

Steamer's crew consists of the following members: 
One master, 4 mates, 1 boatswain, 2 carpenters, 3 quarter- 
masters, 12 seamen, 1 chief engineer, 3 assistant engineers, 

3 junior engineers, 6 oilers, 3 water tenders, 18 firemen, 9 
coal passers, 1 deck engineer, 1 steward, 1 assistant steward, 

4 cooks, 1 baker, 3 messmen, 2 pantrymen, 12 waiters, 2 
wireless operators and 1 purser. 

Vessel has 12 lifeboats allowed 36 persons each. Twelve 
fire plugs and 2 hand pumps. 

FIRE DRILL 
RAPID RINGING OF SHIP'S BELL 

All crew to report at their proper fire stations, connect 
hose and have same ready to be run in direction as ordered. 

Master in general charge on bridge, with 1 quartermaster 
as aid. Quartermaster on watch at the wheel. 

First officer in charge of deck, and to see that orders of 
master are obeyed. 

Chief engineer in charge of his department. 

Third assistant engineer to take charge of engine room 
and fire pumps with his watch consisting of 1 junior engineer, 
2 oilers, 1 water tender, 6 firemen and 3 coal passers. Fire 
pumps to be started and stopped when directed from bridge. 

Hydrant No. 1 Hydrant No. 4 

Third Officer (in charge) First Engineer (in charge) 

Water Tender No. 1 Seaman No. 3 

Fireman No. 1 Fireman No. 4 

Coal Passer No. 1 Coal Passer No. 4 

Hydrant No. 2 Hydrant No. 5 

Fourth Officer (in charge) Second Engineer (in charge) 

Seaman No. 1 Seaman No. 4 

Fireman No. 2 Fireman No. 5 

Coal Passer No. 2 Officers' Messman 

Hydrant No. 3 Hydrant No. 6 

Boatswain (in charge) Junior Engineer (in charge) 

Seaman No. 2 Seaman No. 5 

Fireman No. 3 Fireman No. 6 

Coal passer No. 3 Firemen's Messman 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 53 



Hydrant No. 7 
Junior Engineer (in charge) 
Seaman No. 6 
Fireman No. 7 
Sailors' Messman 

Hydrant No. 8 
Oiler No. 1 (in charge) 
Seaman No. 7 
Fireman No. 8 
First Pantryman 

Hydrant No. 9 
Oiler No. 2 (in charge) 
Seaman No. 8 
Fireman No. 9 
Second Pantryman 

Hydrant No. 10 
Oiler No. 3 (in charge) 
Seaman No. 9 
Fireman No. 10 
Chief Cook 



Hydrant No. 11 
Oiler No. 4 (in charge) 
Seaman No. 10 
Fireman No. 11 
Second Cook 

Hydrant No. 12 
Second Officer (in charge) 
Water Tender No. 2 
Fireman No. 12 
Third Cook 

Forward Hand Pump 
Quartermaster (in charge) 
Seaman No. 11 
Coal Passer No. 5 
Fourth Cook 

After Hand Pump 
Deck Engineer (in charge) 
Seaman No. 12 
Coal Passer No. 6 
Baker 



Chief carpenter in charge of fire axes forward with 1 
waiter as assistant. 

Second carpenter in charge of fire axes aft with waiter 
No. 2 as assistant. Purser, steward, assistant steward and 
10 waiters to take charge of fire buckets and fire extin- 
guishers, and to take charge of and assure passengers. 

Two wireless operators on watch in radio room. 



BOAT DRILL AND ABANDON SHIP 
SEVERAL SHORT BLASTS OF STEAM WHISTLE 

All boat crews to report at their stations, uncover and 
swing out boats. 

Officer in charge of each boat to see that his proper com- 
plement of crew and passengers report, and that plug is in 
and boat falls clear, ready for lowering. 

Boats shall be loaded quietly without unnecessary 
excitement and overcrowding. 



54 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 



Lifeboats of this class are required to have at least 2 
certificated lifeboat men, and officer in charge shall see that 
the proper men are put in charge of handling the falls for 
lowering the boat. 

Notices shall be posted in every passenger stateroom of 
the number of the boat the passenger is to report to, in case 
of boat drill or to abandon ship. 

Every passenger shall be required immediately after 
leaving port to participate in a boat drill, and also in- 
structed in the proper way to adjust a cork life preserver. 

No boat shall be lowered until ordered by master or a 
proper representative of him. 



STATION BILL FOR BOAT DRILL 



No. 1 Boat (Starboard Side) 

Master (in charge) 

Seaman No. 1 (Cert. Lifeboat Man) 

Fireman No. 1 (Cer. Lifeboat Man) 

Chief Steward 

Oiler No. 1 

Coal Passer No. 1 

Chief Cook 

Wireless Operator 

No. 2 Boat (Port Side) 
Chief Officer (in charge) 
Seaman No. 2 (Cer. Lifeboat Man) 
Fireman No, 3 (Cer. Lifeboat Man) 
First Asst. Engineer 
Water Tender No. 1 
Fireman No. 3 
Baker 
Wireless Operator 

No. 3 Boat (Starboard Side) 
Second Officer (in charge) 
Seaman No. 3 (Cer. Lifeboat Man) 
Fireman No. 4 (Cer. Lifeboat Man) 
Second Asst. Engineer 
Water Tender No. 2 
Fireman No. 6 
Officers' Messman 
Waiter No. 1 



No. 4 Boat (Port Side) 
Third Officer (in charge) 
Seaman No. 4 (Cer. Lifeboat Man) 
Fireman No. 5 (Cer. Lifeboat Man'^ 
Third Asst. Engineer 
Water Tender No. 3 
Fireman No. 7 
Fireman's Messman 
Waiter No. 2 

No. 5 Boat (Starboard Side) 
Fourth Officer (in charge) 
Seaman No. 5 (Cer. Lifeboat Man) 
Fireman No. 8 (Cer. Lifeboat Man) 
Junior Engineer 
Coal Passer No. 2 
Fireman No. 10 
Sailor's Messman 
Waiter No. 3 

No. 6 Boat (Port Side) 
Chief Carpenter (in charge) 
Seaman No. 6 (Cer. Lifeboat Man) 
Fireman No. 9 (Cer. Lifeboat Man) 
Junior Engineer 
Coal Passer No. 3 
Fireman No. 11 
Chief Pantryman 
Waiter No. 4 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 55 



No. 7 Boat (Starboakd Side) 
Second Carpenter (in charge) 
Seaman No. 7 (Cer. Lifeboat Man) 
Fireman No.l2 (Cer. Lifeboat Man) 
Junior Engineer 
Coal Passer No. 4 
Fireman No. 14 
Second Pantrjonan 
Waiter No. 6 

No. 8 Boat (Port Side) 
Boatswain (in charge) 
Seaman No. 8 (Cer. Lifeboat Man) 
Fireman No. 13 (Cer. Lifeboat Man) 
Oiler No. 2 
Coal Passer No. 5 
Deck Engineer 
Waiter No. 5 
Waiter No. 7 

No. 9 Boat (Starboard Side) 
Chief Engineer (in charge) 
Seaman No. 9 (Cer. Lifeboat Man) 
Fireman No. 15 (Cer. Lifeboat Man) 
Oiler No. 3 
Coal Passer No. 6 
Assistant Steward 
Waiter No. 8 
Waiter No. 9 

Sextant Adjustments. — No. 1. To Adjust the Index Glass. — This glass must be 
perpendicular to the plane of the instrument. To prove this, set the vernier to 
about the center of the arc and clamp it. Hold the instrument face up with the 
arc away from you, then look obliquely into the index glass and observe if the arc 
seen direct and its reflection form one continuous line; if so, the glass is perpen- 
dicular to the plane of the instrument, but if the reflected image appears to be 
lower than the other it proves the glass leans backward; if, however, the reflected 
image appears to be higher, the glass leans forward. 

No. 2. Adjustment of the Horizon Glass. — This glass must also be perpendicular 
to the plane of the instrument. To test this, let the two zeros cut, and holding 
the instrument almost horizontal look at the horizon line, and note if the direct 
and the reflected images of the horizon line coincide — that is, if they show as an 
unbroken line both in the silvered and clear parts of the glass. If they do, the 
horizon glass is perpendicular, but if they do not, then adjust the glass to the 
required angle by the adjusting screw on back. 

No. 3. — The Two Glasses to be Parallel. — With the two zeros cutting, hold the 
instrument vertically, and if the direct and reflected images of the horizon line 
show as an unbroken line the horizon glass is parallel to the index glass, but if 
they do not show in an unbroken line, adjust the horizon glass by the adjusting 
screw on back. 

No. 4. To Find the Index Error. — Should it prove impossible to obtain a per- 
fect adjustment, find the error of the instrument as follows: Let the two zeros 
cut, then holding the instrument vertically look at the horizon, and gently finger 
the tangent screw so as to move the vernier either forward or backward along fhe 
arc until the image of, and the horizon line itself show in an unbroken line across 
the glass, then the difference between zero on the vernier and zero on the arc will 
be the index error. 



No. 10 Boat (Port Side) 
No. 1 Quartermaster (in charge) 
Seaman No. 10 (Cer. Lifeboat Man) 
Fireman No. 16 (Cer. LifeboatMan) 
Oiler No. 4 
Coal Passer No. 7 
Purser 

Second Cook 
Waiter No. 10 

No. 11 Boat (Starboard Side) 
Quartermaster No. 2 (in charge) 
Seaman No. 11 (Cer. Lifeboat Man) 
Fireman No. 17 (Cer. LifeboatMan) 
Oiler No. 5 
Coal Passer No. 8 
Third Cook 
Waiter No. 11 

No. 12 Boat (Port Side) 
Quartermaster No. 3 (in charge) 
Seaman No. 12 (Cer. Lifeboat Man) 
Fireman No. 18 (Cer. LifeboatMan) 
Oiler No. 6 
Coal Passer No. 9 
Fourth Cook 
Waiter No. 12 



CHAPTER III 
ARITHMETIC OF NAVIGATION 

The arithmetic used in navigation consists of the plain 
rules of arithmetic (addition, subtraction, multiplication 
and division). The addition, subtraction, multiplication 
and division of decimal fractions, and the addition, subtrac- 
tion and division of degrees, minutes and seconds and 
hours, minutes and seconds. 

The plain rules of arithmetic it is taken for granted the 
student knows. 

ADDITION OF DECIMALS 

In addition of decimals place the numbers that are to be 
added so that the decimal points will be over each other, 
and add as a whole number. Place the decimal point in 
answer under the decimal points in the line. 

For example: Add 2894.965; 238.6; and 28.65. 

2894.965 
238.6 
28.65 



(Ans.) 3162.215 

SUBTRACTION OF DECIMALS 

In the subtraction of decimals place the decimal point in 
the numbers so that they will be under each other, and the 
decimal point in the remainder will be under the decimal 
point. 

For example: Subtract 2846.65 from 3897.286. 

3897.286 
-2846.65 



(Ans.) 1050.636 

56 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 57 



MULTIPLICATION OF DECIMALS 

In the multiplication of decimals multiply as in whole 
numbers, and count the number of decimal places there are 
in both numbers, which will be the number of figures count- 
ing from the right, where the decimal point goes in the 
product. 

For example: Multiply 24.48 by 2.6. 

24.48 
X 2.6 



14688 
4896 



(Ans.) 63.648 

DIVISION OF DECIMALS 

In the division of decimals divide as whole riumber. If 
the divisor has more decimals than the dividend, add that 
many decimal zeros to the dividend before making the 
division. To place the decimal point, subtract the number 
of decimals in the divisor from the number of decimal 
places in the dividend, and point off as many decimal places 
in the quotient as there are in the remainder. 

Example: Divide 322 by .26. 

.26)322 . 000 (1238.4 nearly (Ans.) 
26 

62 
52 

100 

78 

220 
208 

120 
104 

16 



58 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

ADDITION OF DEGREES, MINUTES AND SECONDS OR 
HOURS, MINUTES AND SECONDS 

The degrees, minutes and seconds must be directly under 
their like numbers. 

For example: Add together 26° 47' 36'' and 51° 27' 42". 

26° 47' 36" 
51° 27' 42" 



78° 15' 18" (Ans.) 

Adding the seconds gives 78-60 = 18" left, with 1' to 
carry. Adding the minutes gives 75' —60 = 15' left, with 1° 
to carry. Adding degrees gives 78°. 

SUBTRACTION 

The numbers must be directly under their like numbers. 
For example: Subtract 40° 52' 48" from 76° 29' 36". 

76° 29' 36" 
-40° 52'" 18" 



35° 36' 48" (Ans.) 

In subtracting degrees, minutes and seconds or hours, 
minutes and seconds, if the number of seconds in the min- 
uend is less than the number in the subtrahend. You take 
1' or 60" from the minutes and apply it to the minuend. 
In this example 36" is less than 48", so borrow 1' and make 
it 96", we then subtract 48" from this, which leaves 48". 
The minutes will then be 28'. It is now necessary to borrow 
1 °, and add 60' to the minutes for the next subtraction which 
will make 88' — 52' which leaves 36'. The degrees will be 
75° left, from which subtracting 40° leaves 35°. 

SUBTRACTION OF TIME 

The problem of finding longitude resolves itself into 
finding the difference in time at the ship (L. A. T.) 
and at Greenwich (G. A. T.). In finding differences of 
time always put down astronomical time, i.e., a day 
starts at noon and runs through 24 hours till the next 
noon. Put down the day as well as the hours, minutes 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 59 

and seconds. In case it is necessary to borrow, remember 

that a day has 24 hours. 

For example: See Chap. IX., Prob. 1. 

G. A. T. 31st day Ih 58' 13'^ 
L. A. T. 30th day 19h 43' 01" 



6h 15' 12'' (Ans.) 

The 1" may be subtracted from the 13" and tlie 43' from 
58' without difficulty. In subtracting the 19h a day (24h) 
is borrowed in the minuend making 25h ; the days left in the 
minuend being 30d. 

Example: See Chap. IX., Prob. 9. 

G. A. T. 15d 4h 36' 00" 
L. A. T. 14d 19h 25' 27" 



9h 10' 33" (Ans.) 

Borrow 1' or 60" and subtract 27" leaves 33". The 
minutes left will be 35. Borrow a day or 24h, making 28h, 
subtracting 19h leaves 9h. 

DIVISION 

In dividing, if there is any remainder it should be changed 
into the next smaller unit. 

Example: Divide 38° 57' 12" by 2. 

2 )38° 57' 12" 
19° 28' 36" (Ans.) 

Two into 57' goes 28 times and 1' remainder. This is 
changed to 60" and added to the 12" making 72". Two into 
72 goes 36 times. 

To change longitude in time to longitude in degrees, 
minutes, etc., and vice versa, it should be noted that 

360°=24h; 
15°= Ih 

1°=4' 
15' =1' 

1' =4"; 



60 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

To change time to arc : 

Multiply the hours by 15, gives degrees. 

Divide minutes of time by 4, gives degrees. 

Remaining minutes of time multipUed by 15 gives min- 
utes of arc. 

Divide seconds of time by 4, gives minutes of arc. 

Remaining seconds of time multiplied by 15 gives seconds 
of arc. 

Example: Change 9h 37' 14" to are. 

9x15 = 135° 
37 divided by 4 =9° and 1' remaining 

1X15= 15' 

14 divided by 4 = 3' and 2" remaining 

2X15= 30" 



144° 18' 30" (Ans.) 

Example: Change llh 15' 26" to arc. 

11 4)lj5 and 3 remaining 4 )26 and 2 remaining 
X 15 3° 15 6' 15 

165 165 45' 15 30" 



168° 51' 

Ans. 168° 51' 30" 
To change arc to time: 
Divide degrees by 15, gives hours. 
Remaining degrees multiplied by 4, gives minutes. 
Divide minutes of arc by 15, gives minutes of time. 
Remaining minutes of arc multiplied by 4, gives seconds 
of time. 

Divide seconds of arc by 15, gives seconds of time. 

Example: Change 81° 48' 30" to time. ' 



15)81 (5h 6x4=24' 

75 15)48( 3' 

6 remaining 45 27' 


3x4 = 12" 

15)30( 2" 

14" 


3 remaininfic 





Ans. 5h 27' 14" 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 61 

EXPLANATION OF THE AMERICAN NAUTICAL ALMANAC 
FOR THE YEAR 1919 

Pages 2 to 3 is the Right Ascension of Mean Sun at Green- 
wich Mean Noon, and the table below is the correction to be 
added for Greenwich Mean Time. 

For example: G. M. T. Feb. 18th, 6h 28'. Required 
Sun's Right Ascension. 

Sun's Right Ascension Feb. 18th 21h 49' 36" 
Corr. for G. M. T. 6h 28' +___r_04^ 

S. R. A. 21h 50' 40" 

Pages 6 to 29 is the Sun's Declination, Equation of Time, 
and Semi-diameter for Greenwich Mean Noon. 

The declination and equation of time are given for every 
day of the year, and on the even hour. 

The declination is read in degrees and minutes and tenths 
of minutes, the sign + means North declination, the sign — 
means South declination. 

The equation of time is read in minutes and seconds and 
tenths of seconds, the sign+means to add to mean time, 
the sign— means to subtract from mean time. 

To find the sun's declination and equation of time use 
always the Greenwich Mean Time; using the nearest 0.1 
hour. The hourly difference will be found for each date at 
the bottom of each date. Take out the declination for the 
nearest even hour that has passed. Add to this a correction 
which the hourly difference multiplied by the difference in 
time since the last even hour, expressed in tenths of an hour, 
if the decimation is increasing. If the decHnation is decreas- 
ing, the correction should be subtracted. 

For example: Feb. 18, 1919. G. M. T. 9h 14'. Re- 
quired declination and equation of time. 

Decl. for the 18th day, 8th hour 11° 46'.9 S 

Hourly difference 0'.9 

Corr. for 1.2 hours =0'.9x 1.2 == I'.l decreasing 

Decl. for 18th day 9.2 hours 11° 45'.8 S 

Eq. of time 18th day 8th hour -14' 6".8 

Hourly diff. 0".2 

Corr. for 1.2 hours = 0.2x1.2 = 0".2 decreasing 

Eq. of time for 18th day 9.2 hours - 14' 6".6 

or -14' 07" 



62 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

The semi-diameter is given for every 10 days and is in 
minutes and tenths and hundredths of minutes. Read 
semi-diameter to nearest date, and multiply the nearest 
tenth by 6 to give seconds. 

For example: Required S. D. for Feb. 18th. 

In N. A. nearest date given is Feb 21st = 16'.20 
Therefore S. D. =16' 12" 

Pages 30 to 75 is the Moon's Right Ascension, Declina- 
tion, Semi-diameter and Horizontal Parallax given for each 
day, and on the even hour of that day. 

The declination and right ascension are accompanied 
by the difference or change in every 2 hours; by means of 
these differences interpolation may be made to any Green- 
wich Mean Time by Table IV (Almanac) pages 112-114, 
using the difference in 2 hours at top of page, and the interval 
in minutes from nearest even hour on the left-hand side of 
page. 

For example: Feb. 18th, G. M. T., 8h 15'. Required 
Moon's Declination. 

Moon's Dec. 18d for 8h. 9° 0'.4 S Change 208 
Corr. Table IV -f- 2'.6 Decl. increasing 

True Decl. 9° 3'.0 S or 9° 03' 00" S 

For same Horizontal Parallax is 54 . 5 
Semi-diameter 14 . 9 

Pages 76 to 77 is the time of Moon's Transit for Meridian 
of Greenwich. 

To find time of transit in any other Meridian, enter 
Table IV (Almanac). Take the change of transit in small 
figures between the dates at top of page, and the longitude 
in time at right-hand side and read the correction. 

For example: Required time of Moon's Transit on Feb. 
18th in Longitude 90° West. 
Long. 90° = Long, in time 6h. 

Moon's Trans. 18d at Greenwich = 15h 03' 
Corr. from Table IV = + H' 



Time of Trans. Long. 90° = 15h 14' 

Correction is always to be added in West Longitude, suL 
tracted in East Longitude. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 63 

Pages 78 to 98 is the Right Ascension, DecHnation, and 
time of transit given for Greenwich Noon, of the planets 
'' Venus," '' Mars," " Jupiter," and " Saturn." 

The interpolations for finding at any other meridian are 
made by using Table IV (N. A.) with G. M. T. at right- 
hand side, and the difference at top of page. 

For example : Required Right Ascension and Declination 
of planet " Venus " G. M. T. Feb. 18th, 8h 15'. 

R. A. 18d = 23h 23' 00" Change 273 
Corr. Table IV = + 1' 33" R. A. increasing 



Corr. R. A. = 

Decl. 18d 
Corr. Table IV = 


23h 24' 33" 

5° 26.4 S 
10'.4 


Change 304 
Decl. decreasing 



True Decl. = 5° 16'.0 S 

Pages 94 to 95 is the Right Ascension and Declination for 
fixed stars given for each month. 

As the Declination and Right Ascension of a fixed star 
has a very small annual change, it will be close enough for 
practical purposes to take it for the month. 

Example : Required Declination and Right Ascension * 
" Spica " on Feb. 18th. 

Declination 10° 44' 30" S. Right Ascension 13h 20' 58". 
The balance of the tables explain themselves. 

EXPLANATION OF TABLES IN BOWDITCH NAVIGATOR 

OR EPITOME 

TABLE 2 

Is to find the difference of latitude and departure in 
miles for any course in degrees. 

The degrees of the course are found at top of page from 
0° to 45°. 

The degrees of the course are found at bottom of page 
from 45° to 90°. 

When the course is less than 45° read the table as follows: 
Distance in first column. Difference of latitude in second 
column. Departure in third column. 



64 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

When the course is more than 45° read the table as fol- 
lows: Distance in first column. Departure in second col- 
umn. Difference of latitude in third column. 

For example: Course N 38° E. Distance 48 miles. Diff. 
lat. will be 37.8 N. Departure 29.6 E. 

Course N 52° E. Distance 48 miles. Diff. lat. will be 
29.6 N. Departure 37.8 E. 

To find the difference of longitude ship has made, look 
for middle latitude as the course, and the departiu"e in miles 
in the latitude column, in the distance column opposite will 
be the difference of longitude in minutes. 

For example: Middle Lat. 38°. Departure 105.6 miles. 
At 38° look for 105.6 in latitude column, which will equal 
134', which is the difference of longitude in minutes. By- 
dividing this by 60, we obtain Diff. Long. 2° 14'. 

Middle Lat. 52°. Departure 105.6 miles. By same rule 
we find distance 171', or difference of longitude 2° 51'. 

To find course and distance ship has run, compare differ- 
ence of latitude in miles and departure in miles as close as 
possible, course will be found from top of page if latitude is 
greatest, from bottom if departure is greatest, and distance 
will be found on side in distance column. 

For example: Diff. Lat. 151.3. Departure 118.2. Com- 
paring these we find course 38° distance 192 miles. 

Diff. Lat. 118.2. Departure 15L3. We find course 52° 
distance 192 miles. 

TABLE 3 

Used in Mercators sailing for finding the Meridional 
difference of latitude. 

The degrees of latitude are read from top of page, min- 
utes from side. 

For example: 

Lat. A. 28° 46 Mer. Parts Table 3 = 1792 . 2 
Lat. B. 72° 13 Mer. Parts Table 3 =6354.8 

The meridional parts are to be added together when 
degrees and minutes of latitude are added, subtracted when 
degrees and minutes of latitude are subtracted. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 65 



TABLE 7 

Is to convert arc into time and the reverse. 
There are 4' of time to 1° of arc, and 4'' of time to V of 
arc, and this table is based on this principle. 

For example : To turn Long. 94° 32' into time. By figures 
we multiply 94 by 4 and divide by 60, or 94 X4 = 376 divided 
by 60 = 6h 16^ The same rule applies for the minutes, so 
32x4 = 128 divided by 60=2' 8''. By adding these two 
together we get 6h 18' 8" longitude in time. 

By using Tibbie 7 we find that 94°=6h 16' and that 
32' =2' 8". By adding these together we get the same re- 
sult as above. 

The use of this table reduces the amount of figures in 
computing considerably, but the student should under- 
stand the principle it is based on. 

To turn longitude in time into degrees and minutes 
proceed in figures as follows : 

Multiply hours by 60 and add the minutes or 6hx60 = 
360' -1-18' =378'. Divide result by 4, or 378' divided by 
4 = 94° with 2' left over. Reduce minutes to seconds by 
same rule and add seconds. Or 2'x60 = 120"+8" = 128", 
divided by 4 =32' or Long. 94° 32'. 

To use Table 7 proceed as follows : 

Take the hour and nearest minute that can be found, 
which will be 6h 16' will = 94°. We then have 2' 8" left over. 
Looking for 2' 8" we find 32' or Long. 94° 32'. 

When using this table remember that degrees of arc are 
read as hours and minutes of time, minutes of arc as minutes 
and seconds of time, and seconds of arc as seconds and t^" 
of time. 

TABLE 11 

Is used to find the time of Moon's Meridian Passage over 
any Meridian. 

The difference between Moon's Transit is found from 
top of page, and longitude of place at side. 

The numbers taken from this table are to be added to the 
time of Greenwich transit in West longitude, subtracted in 
East longitude. 



66 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



TABLE 20A 

Is the Mean Refraction. This table is used for the stars 
only. 

The apparent altitude is read in first colunm, and the 
refraction will be found opposite to it. 

The refraction is always to be subtracted from apparent 
altitude. 

By apparent altitude is meant, the observed altitude 
corrected for Index Error if any, and Dip. 

For example: Appar. Alt. 19° 12'=Refr. 2' 46'' to be 
subtracted. 

TABLE 20B 

Is the correction for the Sun's apparent altitude for 
Refraction and Parallax, always to be subtracted. 

The apparent altitude is the observed altitude corrected 
for Index Error if any, Semi-diameter and Dip. 

For example: Appar. Alt. 28° 49'=Refr. and Par.-l' 
38''. 

TABLE 24 

Is the correction for the Moon's Apparent Altitude for 
Parallax and Refraction. 

With the Horizontal Parallax as found in Almanac at 
top of page and apparent altitude at side, read the cor- 
rection. 

This correction is always to be added to Appar. Alt. 

Example: H. P. 54.9 Moon's Appar. Alt. 22° 12' = Par. 
andRefr.+48'30". 

TABLE 26 

Is the variation of altitude in 1' from Meridian Pas- 
sage. 

It is used for finding the latitude by Ex-Meridian obser- 
vations of a heavenly body. 

With dechnation to nearest degree at top of page, and 
latitude to nearest degree at side, the variation of altitude 
in 1' will be read. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 67 

(Note) Notice whether latitude and declination are 
same or contrary names. 

Example : 

Lat. 28° N. Decl. 18° S = Variation 2".3. 

By squaring the number of minutes from noon, and mul- 
tiplying same by this number, will give correction for sun's 
altitude always to be added. 

For example: Time 12' from noon = 12 Xl2 = 144x2".3 
= 331" or b' 31'' altitude correction to be added. 

TABLE 27 

Is the reduction to be applied to altitudes near the 
meridian. 

This table is based on the principle of the number of 
minutes from noon squared, multiplied by number from 
Table 26= Alt. Corr. 

Taking the number found in Table 26 in previous exam- 
ple 2".3 and time from noon 12', enter Table 27 with 12' 
at top of page and 2.0 on side, we find 4' 48" alt. corr. By 
interpolating between this and number below would give 
5' 31" alt. corr., if 2.3 was used. 

By squaring minutes and multiplying by number from 
Table 26 eliminates this table. 



TABLE 42 

Is the logarithms of numbers from 1 to 9999. 

For finding the logarithm of a number proceed as follows : 
1, 2, or 3 figures in the number the logarithm will be read 
alongside of the number in the coliimi.. 

Four figures in the number, the first 3 numbers will be 
read on the side and the last number from top of page. Five 
figures in the number, the first 4 numbers as above; the 
fifth is obtained by interpolation. 

In interpolation, the difference " D '' between the logs 
of the nearest four-figure numbers, smaller and larger 
respectively, is found and divided by 10. This is mul- 
tiplied by the last figure to give difference d. d is then 
added to the smaller four-figure log. 



68 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

For example: To find log of 4.8883. 

Log. 4.888 = 0.68913 
Log. 4.889=0.68922 



D= 9 

c? = 3X.9=2.7or3 
Log. 4.8880 = 0" 68913 
d= 3 



Log. 4.8883=0.68916 

Every logarithm has an index number i.e., the number in 
front of the decimal point; which is found by following rule: 

Number between and 1 Index number is 

Number between 1 and 10 Index number is 1 

Number between 10 and 100 Index number is 2 

Number between 100 and 1000 Index number is 3 

For example: 

Log. of 8=0.90309 
Log. of" 28 = 1.44716 
Log. of 365=2.56229 
Log. of 4888=^3.68913 

At the side of the m^in table are small tables of propor- 
tional parts which give the corrections to be added to a log. 
of a four-figure number to give the log. of a five-figm-e num- 
ber. The difference D is at the top of little table in heavy 
type, in the vertical columns are given the difference d. 

For example: To find the log of 4.8883. 

Log. of 4.888 is 0.68913 and D is 9. 

Looking at side of main table and find small table with 
9 in heavy type at top. d for 3 is 3. 

To find log. of 1.2934. 

Log. of 1.293 is 0. 11160 and D is 33. 

Looking at side of main table and find small table with 
33 in heavy type at top. d for 4 is 13. 

Log. 1.2930= 0.11160 
d=+ 13 



Log. 1.2934= 0.11173 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 69 



TABLE 44 

Is the logarithms of the sines, cosecants, tangents, co- 
tangents, secants and cosines. 

From 0° to 45° will be found from top of page and min- 
utes in left-hand column reading down. 

From 45° to 90° will be found on bottom, minutes on 
right-hand side reading up. 

For example: Log. Sine of 18° 48' =9.50821 
Log. Sine of 71° 12' = 9.97619 

To find log. sin, etc. ; to nearest second of angle. 

If angle is larger than 4°; between each two columns of 
logs there is a column of differences, the seconds corre- 
sponding being the left-hand column of minutes. Find the 
log. to the nearest minute, then look down the left-hand 
column to where the number of seconds is found ; then look 
straight across to the vertical column of differences next to 
that in which the log. was found for the correction. The 
correction is to be added if the log. is increasing and vice 
versa. 

If angle is smaller than 4° the difference for 1' is given. 
This must be divided by 60 to give the difference for V\ 
It must then be multiplied by the number of seconds to 
give the correction. 

For example: (See Chap. IX, Prob. 1.) 

Find log. COS. of 73° 39' 24" 

Log. COS. 73° 39'= 9.44948 

0pp. 24 in left-hand col. find in col. of diff. 17 



Since cos. is decreasing sub. 9.44931 

Find log. sin of 59° 38' 42" 

Log. sin 59° 38'; =9.93591 

0pp. 42 in left-hand col. find in col. of diff. 5 



Since sin is increasing add 9 . 93596 



70 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



TABLE 45 

Is the Table for Log. Haversines and Nat. Haversines. 

The Log. Haversine is in Hght type. The Nat. Haver- 
sine in heavy type. 

When looking for Log. Haversine of L. A. T. if the sight 
is A. M., the hours and minutes of time are read from bottom 
of page, and the seconds from right-hand column reading up 
the page. 

When the hours and minutes are taken from the bottom 
of page, the astronomical date will be the date before the 
civil date which is given in example. 

For example: Feb. 9th A. M. at ship. Log. Hav. as 
found from sum of logs. =9.38624. Log. Hav. 9.38624 = 
L. A. T. Feb. 8th, 20h 3' 32'^ 

If the sight is P. M. the hours and minutes will be found 
on top in light type, and the astronomical date will be the 
same as civil date, and the seconds will be found on left- 
hand side reading down the page. 

For example: Feb. 9th P. M. at ship. Log. Hav. 
9.38624 = L. A. T. Feb. 9th, 3h 56' 28''. 

For turning longitude in time into degrees, minutes and 
seconds proceed as follows: Read hours and minutes of 
longitude in time at top, seconds in left-hand column. 

For example: Turn long, in time 3h 56' 28" into arc. 

For 3h 56' we find 59° 0'. For 28" we find +7' or Long. 
59° 7'. 

To find the Nat. Hav. look for Log. Hav. and alongside 
of it will be Nat. Hav. 

For example: Log. Hav. 9.38624 = Nat. Hav. .24335 and 

Nat. Hav. .24335=59° 07' 

Nat. Hav. .24339=59° 07' 15" 

Nat. Hav. . 24342 = 59° 07' 30" 

Nat. Hav. .24345=59° 07' 45" 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 71 



TABLE 46 

IS the correction to be applied to an observed altitude 
of sun or star to find true altitude. 

This table does away with the necessity for applying the 
Semi-diameter, Dip, Refraction and Parallax to sun's alti- 
tude, and dip and refraction to star's altitude. 

The height of eye will be found at top of page, and obs. 
alt. at side, and the correction for sun in first column to be 
added, and to the star in second column to be subtracted. 

For example: Sun^s Obs. Alt. 28° 50' Dip 28' = Corr.+ 
9' 13'' or True Alt. 28° 59' 13". 

Star's Obs. Alt. 28° 50'. Dip 28' = Corr. -6' 57" or 
True Alt. 28° 43' 03". 

This shortens the work of correcting the altitude con- 
siderably, but the student should understand the other 
method before using this table. 



CHAPTER IV 
DAY'S WORK OR SHIP'S POSITION BY DEAD RECKONING 

This problem is to find the ship's position when no 
observations are obtainable. It is accurate as long as the 
proper distance on each course is allowed, and leeway, 
deviation, and variation is correct. 

The leeway is the amount the ship is drifting to leeward 
from the compass course, and is by the judgment of the 
navigator set to so many degrees or points of the compass. 

The deviation is the difference between the compass 
course and the magnetic course, and is explained under 
Deviation of the Compass. 

The variation is the difference between the magnetic 
course and true course, and is explained under Variation 
of the Compass. 

To convert a compass course into a true course allow 
easterly deviation and variation to the right of the com- 
pass course; westerly to the left, always imagining your- 
self standing in the center of the compass and looking 
toward the course you are steering. 

To convert a true course into a compass course, allow 
east to left; west to right. 

The departure course is the bearing of the point of 
departure by a compass. This course must be reversed 
(imagining the ship to have sailed from the point to the 
place you are at time of taking the bearing), and corrected 
for the deviation and variation for the ship's head, making 
the bearing true, and entered in the traverse table as a 
regular course. 

The courses are then corrected for Leeway, deviation 
and variation, and entered in traverse taole. 

The ciu"rent course is the amount and direction the cur- 
rent has set the ship for the day, and is corrected for Vari- 
ation only, and entered in traverse table as a regular course. 

The traverse table is drawn and the true courses and 
distance of each entered. 

72 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 73 

The difference of latitude and departure is found for each 
course and distance, from Table 2 (Bowditch) and entered 
in traverse table. 

The difference of latitude is the amount of latitude 
north or south in miles the ship has run on the course. 

The departure is the amount of easting or westing in 
miles the ship has made on the course. 

The latitude and departure colmnns are then added up 
separately, and the less subtracted from the greater. 

The amount of each left will be the difference of latitude 
north or south, and departure east or west. 

The latitude left is now put down and the difference of 
latitude converted into degrees, minutes and seconds, allow- 
ing 60 miles to 1° of latitude from the equator to the poles. 

Applying this difference of latitude to latitude left will 
give the latitude arrived at. 

A degree of longitude is worth 60 miles on the equator 
or Lat. 0° but on account of the curvature of the earth 
there is no longitude at the poles or Lat. 90°. It is then 
necessary to find the value of a degree of longitude halfway 
between the latitude left and latitude arrived at, we then 
proceed as follows : 

To find Middle Latitude: Add together, Lat. left and 
Lat. in, and divide sum by 2. Answer will be Middle Lati- 
tude. 

The longitude left is now put down and the difference 
of longitude is found as follows : 

Enter Table 2 (Bowditch) with Middle Latitude to 
nearest degree as a regular course, look in the latitude 
column for the difference of departure, and in the distance 
column will be the difference of longitude in minutes. 

Convert this difference of longitude in minutes into 
degrees, minutes and seconds by dividing by 60, and apply to 
longitude left. Answer will be longitude arrived at. 

The latitude and longitude arrived at will be the posi- 
tion of the vessel by dead reckoning. 

To find the true course and distance made in a straight 
line between the places, enter Table 2 (Bowditch) and 
compare the difference of latitude in miles with the depart- 
ure in miles as close as possible. 

Where these two compare will be the course and dis- 
tance. 

The course will be found from top of page if difference 
of latitude is greatest number. 



74 



SIISIPLE RULES AND PROBLEMS IN NAVIGATION 



From bottom of page if Departure is greatest number. 
In the distance column opposite to where these agree 
will be the distance ship has run. 




DLAlGRAM 
For Converting Compass Courses into True Courses 

Allow easterly deviation and variation to the right. 
Allow westerly deviation and variation to the left. 

To Convert a True Course into a Compass Course 

Allow easterly deviation and variation to the left. 
Allow westerly deviation and variation to the right. 

To Convert a True Course into a Magnetic Course 

Allow for variation only, to the left for easterly, to the 
right for westerly. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 



75 



To Convert a Compass Course into a Magnetic Course 

Allow for deviation only, to the right for easterly, to the 
left for westerly. 



PROBLEM NO. 1 

A ship takes her departure from Lat. 28° 14' 00'' N, 
Long. 79° 30 W and sails the following courses: 



Courses 

N 20° W 

S 

S 

S 70° E 

N 40° E 

North 



16° E 

80° W 



Distance 

26 
31 
35 
40 
45 
50 



Deviation 

4° E 

4° W 

6° E 

12° W 

6° E 

3° E 



Variation 

8° W 
8° W 
8° W 
8° W 
8° W 
8° W 



Required Lat. and Long, arrived at. 
distance made? 



True course and 



1st Course 

N 20° W 
Dev. 4° E to right 



2d Course 

S 16° E 
Dev. 4° W to left 



N 16° W 
Var. 8° W to lelt 


S20° E 
Var. 8° W to left 


N 24° W (true) 

3d Course 

S 80° W 
Dev. 6° E to right 


S 28° E (true) 

4th Course 

S 70° E 
Dev. 12° W to left 


S 86° W 
Var 8° W t^ left 


S 82° E 
Var. 8° W to left 


S 78° W (true) 

5th Course 

N 40° E 
Dev. 6° E to right 


East (true) 

6th Course 

North 
Dev. 3° E to right 


N 46° E 
Var. 8° W to left 


N 3° E 
Var. 8° W to left 



N 38° E (true) 



N 5° W (true) 



76 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


N 24° W 


26 


23.8 






10.6 


S 28° E 


31 




27.4 


14.6 




S 78° W 


35 




7.3 




34.2 


East 


40 






40.0 




N 38° E 


45 


35.5 




27.7 




N 5° W 


50 


49.8 


34.7 


82.3 


4.4 




109.1 


49.2 






34.7 




49.2 





Diff. Lat. 74.4 N Dep. 33.1E 

Latitude left 28° 14' 00^' N 
Diff. Lat. 1° 14' 24'' N 



Latitude in 29° 28' 24" N 



2)57° 42' 24" 



Middle Lat. 28° 51' 12" or 29° 

Longitude left 79° 30' W 
Diff. Long. 38' E 



Longitude in 78° 52' W 
True coui^se N 24° E. Distance 81 miles. 

PROBLEM NO. 2 

Ship takes her departure from a point in Lat. 37° 03' N 
Long. 9° 00 W bearing by compass N 48° E distance 15 
miles. Ship's head S 67° W. 

Courses Distance Wind Leeway Deviation Variation 



S 67° W 


45 


N W 


6° 


11° W 


22° W 


N 39° W 


49 


S W 


3° 


17° W 


22° W 


N 22° W 


38 


West 


9° 


11° W 


22° W 


N 56° W 


31 


S W 


14° 


20° W 


22° W 


S 39° W 


36 


S E 


11° 


6° W 


22° W 


S 84° W 


41 


South 


6° 


14° W 


22° W 



Current set S 65° W (Corr. Mgc.) 8 miles for day. 
Required Lat. and Long, arrived at. True course and 
distance made? 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 



77 



PROBLEM NO. 2 

Method of Converting Compass Courses into True Courses 
Before Entering in Traverse Table 



No. 1 

Bearing course N 48"" E to be 

reversed and read 

S. 48° W 
Dev. 11° W to left 



S 37° W 
Var. 22° W to left 



S 15° W (true) 



No. 2 

S 67° W 

6° Leeway to left 



S 61° W 
Dev. 11° W to left 



S 50° W 
Var. 22° W to left 



S 28° W (true) 



No. 3 

N 39° W 

3° Leeway to right 



N 36° W 

17° W Dev. to left 



N 53° W 

22° W Var. to left 



N 75° W (true) 

No. 5 

N 56° W 

14° Leeway to right 



N 42° W 

20° W Dev. to left 



N 62° W 

22° |W Var. to left 



No. 4 

N 22° W 

9° Leeway to right 



N 13° W 

11° W Dev. to left 



N 24° W 

22° W Var. to left 



N 46° W (true) 

No. 6 

S 39° W 

11° Leeway to right 



S 50° W 

6° W Dev. to left 



S 44° W 
122° W Dev. to left 



N 84° W (true) 



S 22° W (true) 



78 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

No. 7 

S 84° W No. 8 Current 

6° Leeway to right S 65° W set of current 

magnetic 



W 90° 22° W Variation 

14° W Dev. to left 

S 43° W set of cur. true 



S 76° W 

22° W Var. to left 



S 54° W (true) 

The true courses are now entered in traverse table with 
their distance in the distance column, and the difference of 
latitude and departure found for each in Table 2. 

ANSWER TO PROBLEM NO. 2 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East West 


S 15° W 


15 




14.5 


3.9 


S 28° W 


45 




39.7 


21.1 


N 75° W 


49 


12.7 




47.3 


N 46° W 


38 


26.4 




27.3 


N 84° W 


31 


3.2 




30.8 


S 22° W 


36 




33.4 


13.5 


S 54° W 


41 




24.1 


33.2 


S 43° W 


8 




5.9 


5.5 



42.3 117.6 Dep. 182. 6W 

42.3 



Diff. Lat. 75.3 S 



Lat. 


left 


37° 


03' 


00" 


N 




Diff. 


Lat. 
in 


, 1° 


15' 


18" 


S 

N 




Lat. 


35° 


47' 


42" 




Lat. 


left 


37° 


03' 




— 






2)72° 


50' 


42" 




Mid, 


. Lat, 


. 36° 


25' 


21" 


or 


36° 


Long. 


left 9 


° 00 


1' W 






Diff . Long. 3 


° 46 


' w 







Long, in 12° 46' W 
True course S 68°V\". Distance 197 miles. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 79 

PROBLEM NO. 3 

A ship takes her departure from a point in Lat. 28° 16' 
15'' N Long. 93° 26' W and sails the following courses: 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


North 


50 


West 


4° 


6° E 


18° W 


N 20° W 


52 


West 


5° 


8° W 


18° W 


West 


53 


Noirh 


6° 


7° E 


18° W 


S 49° W 


54 


North 


r ■ 


8° W 


18° W 


S 79° W 


55 


North 


7° 


9° E 


18° W 


South 


56 


West 


20° 


7° E 


18° W 


S 10° E 


57 


West 


8° 


6° W 


18° W 



Current set east (Corr. Mgc.) 8 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made. 

ANSWER TO PROBLEM NO. 3 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 




South 


East 


West 


N 8° 


W 


50 


49.5 








7.0 


N 41° 


W 


52 


39.2 








34.1 


S "73° 


w 


53 






15.5 




50.7 


S 16° 


w 


54 






51.9 




14.9 


S 63° 


w 


55 






25.0 




49.0 


S 31° 


E 


56 






48.0 


28.8 




S 42° 


E 


57 






42.4 


38.1 




N 72° 


E 


8 


2.5 






7.6 










91.2 




182.8 
91.2 


74.5 


155.7 

74.5 








Diff. Lat 


91. 6S 


Dep. 


81. 2W 






Lat left 


28° 


16' 


15" N 










Diff. Lat. 
Jifit. in 


1° 


31' 


36" S 








26° 


44' 


39" N 








Lat. left 
Mid. Lat. 


28° 


16' 


15" 


27° 






2)55° 


00' 


54" 






27° 


30' 


27" or 








Long 


. left 93° 


26' W 










Diff. 


Lon. 


1° 


31' W 







Long, in 94° 57' W 
True course S 42° W. Distance 123 miles. 



80 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 4 

A ship takes her departure from a point in Lat. 21° 12' 
N Long. 8° 15' E bearing by Compass N 20° W. Distance 
12 miles. Ship's head S 45° W. 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


S 45° W 


40 


South 


3° 


8° E 


7° W 


S 80° W 


41 


South 


8° 


4° E 


7° W 


N 75° W 


42 


S W 


4° 


5° E 


7° W 


N 45° W 


43 


West 


3° 


3° W 


7° W 


North 


44 


East 


2° 


4° W 


7° W 


N 10° E 


45 


East 


3° 


5° E 


7° W 



Current set east (Corr. Mgc.) 12 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made? 



ANSWER TO PROBLEM NO. 4 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


S 19° E 


12 




11.3 


3.9 




S 49° W 


40 




26.2 




30.2 


S 85° W 


41 




3.6 




40.8 


N 73° W 


42 


12.3 






40.2 


N 52° W 


43 


26.5 






33.9 


N 13° W 


44 


42.9 






9.9 


N 5° E 


45 


44.8 




3.9 




N 83° E 


12 


1.5 




11.9 





128.0 41.1 
41.1 



19.7 



155.0 
19.7 



Diff. Lat. 
Lat. left 
Diff. Lat. 

Lat. in 
Lat. left 



86.9 N 
21° 12' 
1° 26' 



Dep. 135.3V, 



00" N 
54'' N 



22° 
21° 



38' 54" N 
12' 



2 )43° 50' 54" 
Mid. Lat. 21° 55' 27" or 22'' 
Long, left 8° 15' E 
Diff. Long. 2° 26' W 

Long, in 5° 49 E 
True course N 57° W. Distance 161 miles. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 



81 



PROBLEM NO. 5 

A ship takes her departure from a point in Lat. 18° 14' 
12'' S Long. 156° 12' E bearing by compass N 89° E dis- 
tance 12 miles. Ship's head North. 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


North 


60 


East 


2° 


12° W 


6° E 


N 20° W 


61 


N E 


4° 


8° W 


6° E 


N 50° W 


62 


North 


3° 


4° E 


6° E 


N 80° W 


63 


North 


4° 


5° E 


6° E 


S 80° W 


64 


N W 


5° 


6° W 


6° E 


S 15° W 


65 


West 


4° 


14° W 


6° E 



Current set S 15° E (Corr. Mgc.) 18 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made? 



ANSWER TO PROBLEM NO. 5 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


S 83° W 


12 




1.5 




11.9 


N 8° W 


60 


59.4 






8.4 


N 26° W 


61 


54.8 






26.7 


N 43° W 


62 


45.3 






42.3 


N 73° W 


63 


18.4 






60.2 


S 75° W 


64 




16.6 




61.8 


S 3° W 


65 




64.9 




3.4 


S 9° E 


18 




17.8 


2.8 





177.9 
100.8 



100.8 



2.8 



214.7 

2.8 



Diff. Lat. 
Lat. left 
Diff. Lat. 

Lat. in 
Lat. left 



77.1 N 
18° 14' 
1° 17' 



16° 

18° 



57' 
14' 



Dep, 211.9W 



12" S 

06" N 



06" S 
12" 



2)35° 11' 18^ 



Mid. Lat. 17° 35' 
Long, left 156° 
Diff. Long. 3° 

Long, in T52° 29^E 

True course N 70° W. Distance 225 miles. 



39" or 18° 
12' E 
43' W 



82 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 6 

A ship takes her departure from a point in Lat. 62° 12' S 
Long. 171° 12' E bearing by compass East distance 12 miles. 
Ship's head S 15° W. 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


S 15° W 


62 


West 


4° 


8° W 


18° E 


South 


64 


S W 


5° 


9° W 


18° E 


West 


66 


North 


6° 


7° E 


18° E 


N 45° W 


68 


West 


3° 


19° W 


18° E 


S 59° W 


70 


South 


6° 


8° W 


18° E 


N 50° W 


72 


s w 


7° 


10° w 


18° E 



Current set S 15° E (Corr. Mgc.) 18 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made? 

ANSWER TO PROBLEM NO. 6 



Corrected 


Distance 


Difference Lat, 


Departure 


Courses 




North 


South 


East 


West 


N 80° W 


12 


2.1 






11.8 


S 21° W 


62 




57.9 




22.2 


S 4° W 


64 




63.8 




4.5 


N 71° W 


66 


21.5 






62.4 


N 43° W 


68 


49.7 






46.4 


S 75° W 


70 




18.1 




67.6 


N 35° W 


72 


59.0 






41.3 


S 3° W 


18 




18.0 




0.9 



132.3 



157.8 
132.3 



Dep. 257. IW 



Lat. left 
Diff. Lat. 

Lat. in 
Lat left 



Diff. Lat. 
62° 



62° 
62° 



25.5 S 
12' 00'' S 
25' 30" S 

" 30" S 



37' 
12' 



2)124° 49' 



Mid. Lat 62° 24' 
Long, left 171° 12' E 
Diff. Long. 9° 08' W 

Long, in 
True course S 84° W. 



30" 

45" or 62° 



162° 04' E 
Distance 258 miles. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 



83 



PROBLEM NO. 7 

A ship takes her departure from a point in Lat. 36° 56' 
N Long. 75° 5r W bearing by compass N 67° W distance 7 
miles. Ship's head S 56° E. 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


S 56° E 


50 


East 


3° 


4° W 


8° E 


S 23° E 


40 


East 


2° 


2° W 


8° E 


South 


20 


East 


4" 


12° W 


8° E 


East 


60 


North 


8° 


3" E 


8° E 


N 73° E 


30 


North 


4° 


4° W 


8° E 


N 51° E 


40 


North 


3° 


3" E 


8° E 



Current set S 46° W (Corr. Mgc.) 14 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made? 

ANSWER TO PROBLEM NO. 7 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


S 63° E 


7 




3.2 


6.2 




S 49° E 


50 




32.8 


37.7 




S 15° E 


40 




38.6 


10.4 




South 


20 




20.0 






S 71° E 


60 




19.5 


56.7 




N 81° E 


30 


4.7 




29.6 




N 65° E 


40 


16.9 




36.3 




S 54° W 


14 




8.2 




11.3 






21.6 


122.3 
21.6 


176.9 
11.3 


11.3 



Diff. Lat. 100.7 S 165.6 Dep. E 
Lat. left 36° 56' 00" N 

Diff. Lat. 1° 40' 42" S 



Lat. in 



35° 15' 18" N 



2)72° 1 1' 18" 
Mid. Lat. 36° 05' 39" or 36° 
Long, left 75° 51' W 

Diff. Long. 3° 25' E 



Long, in 72° 26' W 

True course S 59° E. Distance 193 miles. 



asB 



BSBi 



84 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 8 

A ship takes her departure from a point in Lat. 0° 
2r N Long. 178° 2r E bearing by compass S 21° E distance 
13 miles. Ship's head N 18° E. 



Courses 


Distance 


Wind 


Leewav 


Deviation 


Variation 


N 18° E 


60 


East 


4° 


7° E 


9° w 


N 3° W 


61 


N E 


5° 


4° E 


r w 


N 45° W 


62 


N E 


3° 


1° W 


9° W 


Vv^est 


63 


North 


2° 


6° E 


9° W 


S 50° W 


64 


N W 


1° 


2° E 


9° W 


South 


65 


West 


2° 


6° E 


9° W 



Current set S 15° E (Corr. :\Igc.) 24 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made? 



ANSWER TO PROBLEM NO. 8 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


N 23° 


W 


13 


12.0 






5.1 


N 12° 


E 


60 


58.7 




12.5 




N 13° 


W 


61 


59.4 






13.7 


N 58° 


W 


62 


32.9 






52.6 


S 85° 


W 


63 




5.5 




62.8 


S 42° 


W 


64 




47.6 




42.8 


S 5° 


E 


65 




64.8 


5.7 




S 24° 


E 


24 




21.9 


9.8 










163.0 


139.8 


28.0 


177.0 








139.8 






28.0 






Diff. Lat. 


23.2 N 


Dep. 


149. OW 






Lat. left 


0° 


21' 00'^ 


N 








Diff. Lat. 
Lat. in 




23' 12'' 


N 

N 






0° 


44' 12" 






2)1° 


05' 12" 








Mid. Lat. 




32' 36" 


or V 








Long, left 


178° 21' 


E 








Diff. Long. 


2° 29' 


W 





Long, in 175° 52' E 

True course N 81'' W. Distance 151 miles. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 



85 



PROBLEM NO. 9 

A ship takes her departure from a point in Lat. 3° 10' 
W S Long. 0° 15' W bearing by compass N 10° W distance 
14 miles. Ship's head S 15° W. 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


S 15° W 


40 


S E 


4° 


3° W 


40° E 


S 15° E 


41 


East 


5° 


8° W 


40° E 


East 


42 


South 


6° 


1° E 


40° E 


N 70° E 


43 


South 


4° 


4° W 


40° E 


N 45° E 


44 


North 


2° 


1° E 


40° E 


N 15° E 


45 


East 


1° 


2° E 


40° E 



Current set N 16° W (Corr. Mgc.) 18 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made? 



ANSWER TO PROBLEM NO. 9 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


S 27° W 


14 




12.5 




6.4 


S 56° W 


40 




22.4 




33.2 


S 22° W 


41 




38.0 




15.4 


S 55° E 


42 




24.1 


34.4 




S 78° E 


43 




8.9 


42.1 




N 88° E 


44 


1.5 




44.0 




N 56° E 


45 


25.2 




37.3 




N 24° E 


18 


16.4 




7.3 





43.1 



105.9 
43.1 



165.1 
55.0 



55.0 



Diff. Lat. 62.8 S 110.1 Dep, E 



Lat. left 
Diff. Lat. 

Lat in 



Mid. Lat. 
Long, left 
Diff. Long. 



3° 10' 12" S 

1° 02' 48" S 

4° 13' 00" S 

2 )7° 23' 12" 
3° 41' 36" or 4° 
0° 15' W 
1° 50' E 



Long, in 1° 35' E 

True course S 60° E. Distance 127 miles, 



86 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

PROBLEM NO. 10 

A ship takes her departure from a point in Lat. 67° 15' 
08'' N Long. 112° 12' W bearing by compass S 80° W dis- 
tance 20 miles. Ship's head North. 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


North 


50 


East 


3° 


4° E 


21° W 


N 40° W 


51 


N E 


2° 


9° E 


21° W 


N 15° W 


52 


N E 


3° 


3° E 


21° W 


West 


53 


North 


2° 


26° E 


21° W 


N 70° W 


54 


North 


1° 


2° E 


21° W 


S 89° W 


55 


South 


3° 


4° E 


21° W 



Current set S 22° E (Corr. Mgc.) 14 miles for day. 
Required latitude and longitude arri'/ed at. True course 
and distance made? 

ANSWER TO PROBLEM NO. 10 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


N 63° E 


20 


9.1 




17.8 




N 20° W 


50 


47.0 






17.1 


N 54°* W 


51 


30.0 






41.3 


N 36° W 


52 


42.1 






30.6 


N 87,° W 


53 


2.8 






52.9 


West 


54 








54.0 


S 75° W 


55 




14.2 




53.1 


S 43° E 


14 




10.2 


9.5 






• 


131.0 

24.4 


24.4 


27.3 


249.0 
27.3 



Diff. Lat. 106.6 N Dep. 221. 7W 

Lat. left 67° 15' 08" N 

Diff. Lat. 1° 46' 36" N 



Lat. in 69° 01' 44" N 



2 )136° 16' 52" 
Mid. Lat. 68° 08' 26" or 68'' 
Long, left 112° 12' W 
Diff. Long. 9° 52' W 



Long, m 122° 04' W 

True course N 64° W. Distance 246 miles. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 



87 



PROBLEM NO. 11 

A ship takes her departure from a point in Lat. 0° 00 
Long. 0° 00' bearing by compass South distance 18 miles 
Ship's head East. 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


East 


70 


S E 


2° 


12° E 


18° W 


S 45° E 


71 


South 


8° 


5° E 


18° W 


S 15° E 


72 


East 


3° 


25° E 


18° W 


South 


73 


East 


4° 


8° E 


18° W 


S 10° W 


74 


East 


2° 


4° E 


18° W 


S 45° W 


75 


S E 


r 


6° E 


18° W 



Current set N 8° W (Corr. Mgc.) 19 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made? 



ANSWER TO PROBLEM NO. 11 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


N 6° W 


18 


17.9 






1.9 


N 82° E 


70 


9.7 




69.3 




S 66° E 


71 




28.9 


64.9 




S 5° E 


72 




71.7 


6.3 




S 6° E 


73 




72.6 


7.6 




S 2° E 


74 




74.0 


2.6 




S 34° W 


75 




62.2 




41.9 


N 26° W 


19 


17.1 






8.3 






44.7 


309.4 
44.7 


150.7 
52.1 


52.1 



Difif. Lat. 264.7 8 98.6Dep. E 

Lat. left 0° 00' 00'' 

Diff. Lat. 4° 24' 42" S 



Lat. in 
Mid. Lat. 



2 )4° 24' 4 2" S 
2° 12' 21" or 2° 



Long, left 0° 00' 00" 
Diff. Long. 1° 38' 45" E 



Long, in 1° 38' 45" E 
True course S 20° E. Distance 281 miles. 



88 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

PROBLEM NO. 12 

A ship takes her departure from a point in Lat. 51° 37' 
N Long. 8° 32' W bearing by compass N 45° W distance 12 
miles. Ship's head S 17° W. 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


S 17° W 


26 


West 


3° 


5° E 


24° W 


S 53° W 


30 


N W 


3° 


9° W 


24° W 


S 67° W 


50 


N W 


6° 


12° W 


24° W 


N 3° W 


38 


N W 


9° 


4° W 


24° W 


S 51° E 


32 


s w 


0" 


ir E 


24° W 



Current set N 79° W (Corr. Mgc.) 14 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made? 

ANSWER TO PROBLEM NO. 12 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




Nortli 


South 


East 


West 


S 64° E 


12 




5.3 


10.8 




S 5° E 


26 




25.9 


2.3 




S 17° W 


30 




28.7 




8.8 


S 25° W 


50 




45.3 




21.1 


N 22° W 


38 


35.2 






14.2 


S 64° E 


32 




14.0 


28.8 




S 77° W 


14 




3.1 




13.6 



35.2 122.3 41.9 57.7 
35.2 41.9 



Diff. Lat. 

Lat. left 51° 
Diff. Lat. 1° 


87.1 S Dep. 15. 8W 

37' 00" N 

27' 06" S 


Lat. in 


50° 


09' 54" N 


Mid. Lat. 


2)101° 
50° 


46' 54" 

53' 27" or 51° 



Long, left 8° 32' W 

Diff. Long. 25' W 



Long, in 8° 57' W 

True course S 10° W, Distance 89 miles. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 89 

PROBLEM KO. 13 

A ship takes her departure from a point in Lat. 62° 11' 
N Long 5° 08' E bearing by compass S 28° W distance 10 
miles. Ship's head N 22° W. 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


N 22° W 


39 


N E 


6° 


7° W 


20° W 


N 68° W 


36 


North 


8° 


18° W 


20° W 


S 28° W 


39 


S E 


3° 


9° W 


20° W 


S 11° E 


40 


East 


0° 


3° E 


20° W 


S 6° E 


35 


S W 


11° 


2° E 


20° W 


N 23° E 


31 


N W 


14° 


6° E 


20° W 



Current set S 56° W (Corr. Mgc.) 36 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made? 

ANSWER TO PROBLEM NO. 13 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


N 1° E 


10 


10.0 




0.2 




N 55° W 


39 


22.4 






31.9 


S 66° W 


36 




14.6 




32.9 


S 2° W 


39 




39.0 




1.4 


S 28° E 


40 




35.3 


18.8 




S 35° E 


35 




28.7 


20.1 




N 23° E 


31 


28.5 




12.1 




S 36° W 


36 




29.1 




21.2 



60.9 146.7 51.2 87.4 
60.9 51.2 



Diff. Lat. 85.8 S Dep. 36. 2W 

Lat. left 62° 11' 00'' N 

Diff. Lat. 1° 25' 48" S 

Lat. in 60° 45' 12" N 



2 )122° 56' 12" 

Mid. Lat. 61° 28' 06" or 61° 

Long, left 5° 08' E 

Diff. Long. 1° 15' W 

Long, in 3° 53' E 

True course S 23° W. Distance 93 miles. 



90 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

PROBLEM NO. 14 

A ship takes her departure from a point in Lat. 47° 34' 
IS Long. 52° 40' W bearing by compass N 70° W distance 
17 miles. Ship's head N 84° E. 



Course 


Distance 


Wind 


Leeway 


Deviation 


Variation 


N 84° E 


20 


S E 


14° 


9° E 


31° W 


N 20° E 


33 


East 


6° 


11° E 


31° W 


S 42° E 


35 


N E 


3° 


4° E 


31° W 


N 70° W 


35 


S W 


5° 


6° W 


31° W 


N 53° E 


37 


N W 


3° 


4° E 


31° W 


S 64° E 


28 


N E 


5° 


3° W 


31° W 



Current set N 73° E (Corr. Mgc.) 17 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made? 

ANSWER TO PROBLEM NO. 14 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


N 88° E 


17 


0.6 




17.0 




N 48° E 


20 


13.4 




14.9 




N 6° W 


33 


32.8 






3.4 


S 66° E 


35 




14.2 


32.0 




S 78° W 


35 




7.3 




34.2 


N 29° E 


37 


32.4 




17.9 




N 87° E 


28 


1.5 




28.0 




N 42° E 


17 


12.6 




11.4 








93.3 


21.5 


121.2 


37.6 






21.5 




37.6 






Diff. Lat. 


71.8 IS 


\ Dep. 


83. 6E 






Lat. left 


47° 


34' 00" 


' N 






Diff. Lat. 
Lat. in 


1° 


11' 48'^ 


' N 






48° 


45' 48'' 


' N 






2)96° 


19' 48'^ 








Mid. Lat. 


48° 


09' 54" 


"or 48° 






Long, left 52° 40' W 






Diff. Long. 


2° 05' E 





Long, in 50° 35' W 

True course N 49° E. Distance 111 miles. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 91 

PROBLEM NO. 15 

A ship takes her departure from a point in Lat. 38® 43' 
S Long. IT 35' E bearing by compass S 28° E distance 16 
miles. Ship's head N 56° W. 



Course 


Distance 


Wind 


Leeway 


Deviation 


Variation 


N 56° W 


35 


North 


11° 


16° W 


25° W 


S 34° E 


40 


S W 


3° 


11° E 


25° W 


S 6° W 


41 


S E 


0° 


2° W 


25° W 


N 87° W 


37 


North 


6° 


26° W 


25° W 


N 28° E 


34 


N W 


20° 


8° E 


25° W 


S 11° E 


37 


East 


8° 


3° E 


25° W 



Current set S 56° E (Corr. Mgc.) 39 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made? 

ANSWER TO PROBLEM NO. 16 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


N 69° W 


16 


5.7 






14.9 


S 72° W 


35 




10.8 




33.3 


S 51° E 


40 




25.2 


31.1 




S 21° E 


41 




38.3 


14.7 




S 36° W 


37 




29.9 




21.7 


N 31° E 


34 


29.1 




17.5 




S 25° E 


37 




33.5 


15.6 




S 81° E 


39 




6.1 


38.5 





34.8 143.8 117.4 69.9 
34.8 69.9 



Diff. Lat. 109.0 S 47.5 Dep. E 

Lat. left 38° 43' 00" S 

Diff. Lat. 1° 49' 00^' S 

Lat. in "40° 32' 00'' S 

2)79° 15' 00" 
Mid. Lat. 39° 37' 30" or 40° 

Long, left 77° 35' E 

Diff. Long 1° 02' E 

Long, in 78° 37' E 

True course S 23° E. Distance 119 miles. 



92 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

PROBLEM NO. 16 

A ship takes her departure from a point in Lat. 61° 19' 
N Long. 179° 19' E bearing by compass N 56° W distance 
18 miles. Ship's head N 23° E. 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


N 23° E 


34 


N W 


11° 


6° E 


20° E 


N 56° E 


40 


North 


3° 


16° E 


20° E 


N 86° E 


30 


South 


14° 


21° E 


20° E 


S 23° W 


26 


S E 


28° 


7° W 


20° E 


N 73° W 


30 


North 


20° 


19° W 


20° E 


S 23° E 


36 


S W 


8° 


7° E 


20° E 



Current set S 56° E (Corr. Mgc.) 38 miles for day. 
Required latitude and longitude arrived at. True course 
and distance? 

ANSWER TO PROBLEM NO. 16 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


S 30° E 


18 




15.6 


9.0 




N 60° E 


34 


17.0 




29.4 




S 85° E 


40 




3.5 


39.8 




S 67° E 


30 




11.7 


27.6 




S 64° W 


26 




11.4 




23.4 


S 88° W 


30 




1.0 




30.0 


S 4° E 


36 




35.9 


2.5 




S 36° E 


38 




30.7 


22.3 








17.0 


109.8 
17.0 


130.6 
53.4 


53.4 



Diff. Lat. 92.8 S 77.2 Dep. E 

Lat. left 61° 19' 00'' N 

Diff. Lat. 1° 32' 48" S 

Lat. in 59° 46' 12" N 



2 )121° 05' 12" 
Mid. Lat. 60° 32' 36" or 61 

Long, left 179° 19' E 
Diff. Long. 2° 39' E 

Long, in 178° 02' W 

True course S 40° E. Distance 121 miles. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 93 

PROBLEM NO. 17 

A ship takes her departure from a point in Lat. 40° 19' 
S Long. 9° 44' W bearing by compass East distance 20 
miles. Ship's head N 39° W. 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


N 39° W 


22 


s w 


3° 


3° E 


20° W 


N 23° W 


23 


West 


3° 


8° E 


20° W 


N 23° E 


18 


N W 


6° 


20° E 


20° W 


S 48° E 


19 


N W 


0° 


6° W 


20° W 


S 34° E 


10 


S W 


0° 


9° W 


20° W 


N 3° W 


42 


West 


3° 


14° E 


20° W 



Current set N 73° W (Corr. Mgc.) 36 miles for day. 
Required latitude and longitude arrived at. True course 
and distance 

ANSWER TO PROBLEM NO. 17 



Corrected 


Distance 


Difference Lat 




Departure 


Courses 




North 


South 


East 


West 


S 73° W 


20 




5.8 




19.1 


N 53° W 


22 


13.2 








17.6 


N 32° W 


23 


19.5 








12.2 


N 29° E 


18 


15.7 






8.7 




S 74° E 


19 




5.2 


18.3 




S 63° E 


10 




4.5 


8.9 




N 6° W 


42 


41.8 








4.4 


S 87° W 


36 




1 


.9 




36.0 






90.2 


17.4 


35.9 


89.3 






17.4 








35.9 




Diff. Lat. 


72.8 N 




Dep. 


53. 4W 




Lat. left 


40° 


19' 


00" 


S 






Diff. Lat. 


1° 


12' 


48" 


N 






Lat. in 


39° 

2)79° 


06' 
25' 


12" 
12" 


~S 






Mid. Lat. 


39° 


42' 


36" 


"or 40° 






Long, left 


9° 


44' 


W 






Diff. Long. 
Long, in 


1° 


10' 


W 
~W 






10° 


54' 





True course N 36° W. Distance 90 mile^ 



94 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

PROBLEM NO. 18 

A ship takes her departure from a point in Lat. 49° 42' S 
Long. 178° 42' E and sails the following courses: 

Courses Distance Wind Leeway Deviation Variation 



N 42° E 


35 


S E 


5° 


21° E 


14° E 


N 73° E 


36 


North 


3° 


15° E 


14° E 


S 48° W 


37 


S E 


3° 


15° W 


14° E 


S 17° E 


26 


East 


9° 


13° W 


14° E 


N 8° E 


33 


East 


8° 


18° E 


14° E 


N 14° W 


38 


N E 


3° 


12° E 


14° E 



Current set N 56° E (Corr. Mgc.) 28 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made? 

ANSWER TO PROBLEM NO. 18 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


N 72° E 


35 


10.8 




33.3 




S 75° E 


36 




9.3 


34.8 




S 50° W 


37 




23.8 




28.3 


S 7° E 


26 




25.8 


3.2 




N 32° E 


33 


28.0 




17.5 




N 9° E 


38 


37.5 




5.9 




N 70° E 


28 


9.6 




26.3 








85.9 


58.9 


121.0 


28.3 






58.9 




28.3 






Diff. Lat. 


27.0 N Dep. 


92. 7E 






Lat. left 


49° 


42' 00" 


S 






Diff. Lat. 
Lat. in 




27' 00" 


N 
S 






49° 


15' 00" 






2)98° 


57' 00" 






Mid. Lat. 


49° 


28' 30"' 


or 49^ 






Long, left 178° 42' E 








Diff. Long. 


2° 21' E 







Long, m 178° 57' W 

True course N 73° E. Distance 96 miles. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 95 

PROBLEM NO. 19 

A ship takes her departure from a point in Lat. 28° 14' 
S Long. 102° 16' E bearing by compass S 68° E distance 14 
miles. Ship's head North. 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


North 


60 


West 


4° 


70 -^ 


9° E 


N 28° W 


61 


S W 


5° 


3° E 


9° E 


N 28° E 


62 


East 


3° 


12° E 


9° E 


S 87° E 


63 


North 


2° 


4° W 


9° E 


S 15° E 


64 


S W 


4° 


14° W 


9° E 


East 


65 


North 


3° 


8° W 


9° E 



Current set S 23° W (Corr. Mgc.) 19 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made? 

ANSWER TO PROBLEM NO. 19 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


N 66° W 


14 


5.7 






12.8 


N 6° E 


60 


59.7 




6.3 




N 11° W 


61 


59.9 






11.6 


N 46° E 


62 


43.1 




44.6 




S 80° E 


63 




10.9 


62.0 




S 24° E 


64 




58.5 


26.0 




S 86° E 


65 




4.5 


64.8 




S 32° W 


19 


168.4 


16.1 
90.0 




10.1 




203.7 


34.5 




Diff. Lat. 


90.0 

78.4 N 


Dep. 


34.5 






169.2 E 






Lat. left 


28° 


14' 00" 


S 






Diff. Lat. 


1° 


18' 24" 


N 





Lat. in 26° 55' 36" S 

2y55° 09' 36 ^ 
Mid. Lat. 27° 34' 48" or 28° 

Long, left 102° 16' E 
Diff. Long. 3° 12' E 



Long, in 105° 28' E 

True course N 65° E. Distance 187 niiles. 



96 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

PROBLEM NO. 20 

A ship takes her departure from a point in Lat. 24° 16' 
N Long. 37° 18^ W bearing by compass East distance 9 
miles. Ship's head South. 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


South 


70 


East 


4° 


5° W 


10° E 


S 45° W 


71 


N W 


5° 


3° W 


10° E 


West 


72 


North 


4° 


9° E 


10° E 


N 80° W 


73 


South 


4° 


4° W 


10° E 


S 15° W 


74 


West 


2° 


3° W 


10° E 


N 45° W 


75 


N E 


3° 


8° W 


10° E 



Current set East (Corr. Mgc.) 17 miles for day. 
Required latitude and longitude arrived at. True course 
and distance made? 

ANSWER TO PROBLEM NO. 20 



Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East 


West 


N 85° 


W 


9 


0.8 








9.0 


S 9° 


w 


70 




69 


.1 




11.0 


S 47° 


w 


71 




48.4 




51.9 


N 75° 


w 


72 


18.6 








69.5 


N 70° 


w 


73 


25.0 








68.6 


S 20° 


w 


74 




69.5 




25.3 


N 46° 


w 


75 


52.1 








54.0 


S 80° 


E 


17 




3.0 


16.7 










96.5 


190.0 
96.5 


16.7 


289.3 
16.7 






Diff. Lat. 


93.5 S 


Dep. 


272. 6W 






Lat. left 


24° 


16' 


00" 


■ N 








Diff. Lat. 


1° 


33' 


30" 


' S 








Lat. in 


22° 


42' 


30" 


~N 










2)46° 


58' 


30" 










Mid. Lat. 


23° 


29' 


15" 


""or 23° 








Long, left 


37° 


18' 


W 








Diff. Lor 


^g. 


4° 


56' 


W 








Long, in 




42° 


14' 


W 





True course S 71° W. Distance 288 miles. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 97 

PROBLEM NO. 21 

I Steered S 18° W by Compass, Error 18° E, Var. 7° E, 16 
miles, N 18° W Magnetic, Error 18° E, Var. 7° j], 16 miles. 

How would I have to steer to get back to where I started 
from, and if Cape Flyaway (Lat. 43° 17' N Long. 73° 18' 
E) bore North (True) 21 miles, what would be my position? 

Corrected 
Courses Dist. N S E W 

S 36° W 16 12.9 9.4 

N 11° W 16 15.7 3.1 



15.7 12.9 Dep. 12. 5W 

12.9 



D. Lat. 2.8 N 

Course to steer to get back to point of Departure S 78® 
E 13 miles. 

Cape Flyaway Lat. 43° 17' N Long. 73° 18' E 

Difference Lat. 21' S 



Ship's Position Lat. 42° 56' N Long. 73° 18' E 



PROBLEM NO. 22 

At sea in Lat. 26° 12' N Long. 88° 13' W. Received 
wireless that South Pass Light- Vessel had been adrift 47 
hours. Current setting E. S. E. (Mgc.) 3 miles per hour. 
Now at anchor. Please find Light-Vessel and tow her back 
to her position Lat. 28° 59' N Long. 89° 07' W, Var. 5° E. 

Find true course and distance to Light- Vessel and course 
and distance back to her position. 

N S E W 

66.2 124.5 

Position of Light-Vessel Lat. 28° 59' N 
Diff. Lat. 1° 06' S 



Corrected 




Courses 


Dist. 


S 62° E 


141 



Present Position Light-Vessel 27° 53' N 
Ship's Position Lat. 26° 12' N 



Diff. Lat. 1° 41' N 



98 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



Long, of Light- Vessel 
Diff. Long. 

Present Long, of Light- Vessel 
Ship's Position Long. 



89° 07' W 
2° 21' E 



86° 

88° 



46' W 
13' W 



Diff. Long. 
Diff. Lat. 101 N 



1° 27' E 
Dep. 77.5 E 



Course and distance to Light-Vessel N 38° E 127 miles. 
Course and distance back to Light- Vessel's Station N 62° 
W 141 miles. 



PROBLEM NO. 23 

A ship sailed from Point Neverbudge, Lat. 41° 00' S 
Long. 86° 15' E, the following courses: 

South true 14 miles. 

South by Compass, Error 6° E, Var. 6° W, 14 miles. 
East by Compass, Dev. 4° E, Var. 6° W, 24 miles. 
West by Compass, Dev. 6° E, Var. 6° W, 24 miles. 
North by Compass, Dev. 16° E, Var. 6° W, 28 miles. 
Find course and distance made good and latitude and 
longitude arrived at. 











Difference 


Corrected 


Distance 


Difference Lat. 


Departure 


Courses 




North 


South 


East West 


South 


14 




14.0 




S 6° W 


14 




13.9 


1.5 


N 88° E 


24 


0.8 




24.0 


West 


24 






24.0 


N 10° E 


28 


27.6 




4.9 



28.4 
27.9 



27.9 



28.9 
25.5 



25.5 



Diff. Lat. 



5 N 



Dep. 3.4 E 



Lat. left 41° 00' 00" S Long, left 86° 15' 00" E 
Diff. Lat. 30" N Diff. Long. 4' 30" E 



Lat. Ar. at 40° 59' 30" S Long. Ar. at 86° 19' 30" E 
Mid. Lat. (41°) 

Coiu-se N 81 ° E. Distance 3 miles. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 99 

PROBLEM NO. 24 

From Nantucket Shoals Light Ship (Lat. 40° 37' N Long. 
69° 36' W) bearing North (True) 10 miles. Error 7° W. 
I steered N 75° W by Compass Var. 12° 30' W Dev. 7° 30' 
E for 95 miles. How woiild Block Island S E Light (Lat. 41° 
09' N Long. 71° 33' W) bear True? 



Corrected 
Courses Dist. N 


S 




E 


w 


South 10 

N 80° W 95 16.5 


10 






93.6 


16.5 
10 


10 




Dep. 


93. 6W 


Diff. Lat. 6.5 N 










Nantucket Shoals Light Ship Lat. 
Difference Latitude 




40° 


' 37' 
6' 


00" N 
30" N 


Position of Ship Lat. 
Block Island Light Lat. 


40° 
41° 


43' 
09' 


30" N 
00" N 


Diff. Lat. 

Mid. Lat. 41° Diff. Lat. 25.5 N. 




25' 


30" N 


Nantucket Shoal Lightship Long. 
Diff. Long. 






69° 

2° 


36' W 
04' W 


Position of Ship Long. 
Block Island Light Long. 


71° 
71° 


40' W 
33' W 


Diff. Long. 




7' E 


Dep. 5.3 E. 










True bearing N 12 E 26 miles. 










PROBLEM NO. 


25 









Steer East (Mgc). 

North (True). 

West (True). 

South (Mgc). 
Steamed 12 knots for one hour on each course. 
Variation for the 4 hours 7° W. 



100 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

Find position of ship if you left Lat. 43° 17' N Long. 
73° 14' E. 



Corrected 
Courses 

N 83 E 

North 

West 

S 7° E 




Dist. 
12 
12 
12 
12 




N 

1.5 
12.0 


S 
11.9 


E 
11.9 

1.5 


W 

12.0 










13.5 
11.9 


11.9 


13.4 
12.0 


12.0 






Diff. 


T/at 


. 1.6 N Dep 


. 1.4 E 




Lat. left 
Diff. Lat. 


43° 


17' 


00 
36 


" N 

" N 


Long, left 
Diff. Long. 


73° 


14' E 
2' E 



Lat. Ar. at 43° 18' 36" N Long. Ar. at 73° 16' E 
Course N 41° E. Distance 2 miles. 

PROBLEM NO. 26 

A ship from Point Neverbudge (Lat. 42° 25' N Long. 
86° 15' E), steered the following courses: 

South (True) 14 miles. 

East by Compass, Error 6° E, Var. 6° W, 14 miles. 

N 15° E by Compass, Dev. 9° W, Var. 6° W, 15 miles. 

S 4° W (Mgc), Dev. 7° E, Var. 6° W, 19 miles. 

S 17° E by Compass, Dev. 9° E, Var. 6° W, 25 miles. 

Find course and distance made good and latitude and longi- 
tude arrived at. 



Corrected 










Courses 


Dist. 


N 


s 


E W 


South 


14 




14.0 




S 84° E 


14 




1.5 


13.9 


North 


15 


15 






S 2° E 


19 




19.0 


0.7 


S 14° E 


25 




24.3 


6.0 






15 


58.8 
15.0 


20.6 E Dep. 



Diff. Lat. 43,8 S 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 101 

Lat. left. 42° 25' 00'' N Long, left 86° 15' E 

Diff. Lat. 43' 48" S Diff. Long. 28' E 



Lat. At. at 41° 41' 12" N Long. Ar. at 86° 43' E 
Mid. Lat. 42°. 

Course S 25° E. Distance 48 miles. 



U. S. NAVY METHOD 

A ship takes her departure at Noon heading 210° (p. s. c.) 
with Point Pinos Lighthouse, CaL, abeam distance 7 miles. 
Pat. Log. read 81. 

At 5 P. M. changed course to 280°. Patent Log 50. 

At 8 P. M. changed course to 350°. Patent Log 1. 

At 2 A. M. changed course to 270°. Patent Log 90. 

At 6 A. M. changed course to 180°. Patent Log 47. 

At 9 A. M. changed course to 110°. Patent Log 86. 
At Noon Patent Log read 28. 

Current set for day 60° (Mgc.) at rate of 1^'. 

Variation on all courses 22° E. Use deviation table from 
Page 41 (Bowditch). 

Required Noon position, and course and distance made. 
Point Pinos on California coast. 

First course is bearing. If ship was heading 210° when 
bearing was taken, and lighthouse was abeam, the light- 
house must have been 90° from 210° or to the eastward of 
the ship, being on the California coast. So we find 

210° 
- 90° 



120° bearing of Lighthouse 
+ 180° 



300° bearing reversed. 
Dev. 27° E as per ship's head. 



327° 
Var. 22° E 



True 349° 7 miles. 



102 SIMPLE RULES AND PROBLEMS IN NAVIGATION 







No. 2 




Course 


210' 


Log 5 P.M. 


50 


Dev. 


27° 


+ Log Noon 


-81 




237° 


Dist. 


69 


Var. 


22° 


+ 




True 


259° 


=69 miles. 




No. 3 




No. 4 




280° Log 


50 


350° 




Dev. 4°+ Log 


1 


Dev. 16°- 




284° 


51 


334° 




Var. 22° + 




Var. 22° + 





True 306° Dist. 51 True 356° Dist. 89. 



No. 5 




No. 6 


270° 




180° 


Dev. 10° + 


Dev. 


18° + 


280° 




198° 


Var. 22° + 


Var. 


22° + 



True 302° Dist. 57' True 220° Dist. 39'. 



No. 7 No. 8 

110° 24 hours at If miles per 

Dev. 9°- hour. 

Current 60° 



101° Var. 22" + 
Var. 22°+ 



True 82° Dist. 30' 



True 123° Dist. 42' 



SIMPLE RULES AND PROBLE 


MS IN 


r m 


iVIGATI 


ON 103 


Corrected 


Distance 


Difference Lat. 




Departure 


Courses 




North 


South 




East 


West 


349° 


7 


6.9 








1.3 


259° 


69 




13.2 






67.7 


306° 


51 


30.0 








41.3 


356° 


89 


88.8 








6.2 


302° 


57 


30.2 








48.3 


220° 


39 




29.9 






25.1 


123° 


42 




22.9 




35.2 




82° 


30 


4.2 






29.7 








160.1 


66.0 




64.9 


189.9 




Diff. Lat. 


66. 






Dep.' 


64.9 




94.1 N 


125. OW 




Latitude left 36° 


37' 


55' 


" N 






Diff. Lat. 
Lat. in 


1° 


34' 


06' 


" N 






38° 


12' 


or 


" N 






2)74° 


49' 


56' 








Mid. Lat. 


37° 


24' 


58' 








Long. left 


121° 


56' 


02' 


■' W 






Diff. Long. 


2° 


37' 


00' 


"W 





Long, in 124° 33' 02'' W 

True course 307°. Distance 157 miles. 

U. S. NAVY METHOD 

A ship takes her departure at 4 P. M. heading 93° Dev. 
4° W (p. s. c.) with Nantucket South Shoal Lightship, 
Mass., abeam, distance 9 miles. Patent log read 77. 

At 7 P. M. clianged course to 170° P. L. 16 Dev. 9° W. 
At 11 P. M. changed course to 189° P. L..67 Dev. 10° W. 
At 1A.M. changed course to 115° P. L. 94 Dev. 6° W. 
At 4 A. M. changed course to 70° P. L. 32 Dev. 1° W. 
At 8 A. M. changed course to 90° P. L. 84 Dev. 4° W. 



104 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

Variation on all courses 11° W. 

At noon log read 36. 

Current set 286° (Mgc.) at rate of If miles per hour. 

Required noon position. True course and distance. 

Departure 

West 



Corrected 


Distance 


Difference Lat. 


E 


Courses 




North 


South 


East 


168° 


9 




8.8 


1.9 


78° 


39 


8.1 




38.1 


150° 


51 




44.2 


25.5 


168° 


27 




26.4 


5.6 


98° 


38 




5.3 


37.6 


58° 


52 


27.6 




44.1 


75° 


52 


13.5 




50.2 


275° 


33 


2.9 







2.9 






32.9 


52.1 


84.7 
52.1 


203.0 
32.9 


32.9 



Diff. Lat. 32.6 S 170.1 Dep. East 

Lat. left 40° 37' 05'' N 

Diff. Lat. 32' 36" S 



Lat. in 40° 04' 29" N 



2 )80° 41' 34" 

Mid. Lat. 40° 20' 47" 

Long, left 69° 36' 33" W 

Diff. Long. 3° 42' E 

Long, in 65° 54' 33" W 

True course 101°. Distance 173 miles. 



CHAPTER V 
MERCATORS SAILING 

This problem is to find the course and distance in a 
straight Hne between two places. 

The latitude and longitude A is the point of starting, 
and the latitude and longitude B is the place bound for. 

The latitude A and latitude B and longitude A and longi- 
tude B are put down under each other, and the difference 
between the places is found in degrees, minutes and seconds 
by the following rule: 

Both of the same name, subtract. Different name, add 
the two. 

If the degrees of longitude exceed 180°; subtract total 
from 360°. 

The degrees and minutes are turned into minutes by mul- 
tiplying the degrees by 60, and adding to the result the 
minutes. 

A Mercator chart is constructed on the principle that the 
earth is a flat plane, and the degrees of longitude are equal, 
and the degrees of latitude are increased from the equator 
to the poles to allow for the decrease in the degrees of 
longitude. 

From Table 3 (Bowditch) take out the Meridional Parts 
for the degrees and minutes of each latitude. 

Add or subtract these meridional parts, same as was done 
with the degrees and minutes of latitude in the problem. 

In Table 42 (Bowditch) will be found Logarithms of 
numbers. All logarithms of numbers have an index number 
which is found by table below: 

2 figures in the distance, the index number is 1. 

3 figures in the distance, the index number is 2. 

4 figures in the distance, the index number is 3. 

When the number is of 2 or 3 figures the logarithm is 
read in the column alongside of the number given. 

105 



106 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

When the number has 4 figures the first 3 numbers of 
the figures are read on the side, and the last number at 
top of page. 

Take out from Table 42 logarithm of difference of longi- 
tude in minutes, adding 10 to the index number, and log- 
arithm of meridional parts, index number by rule above. 

Subtract logarithm of meridional parts from logarithm 
of difference of longitude. 

The Logarithm Tangent in Table 44 (Bowditch) that 
agrees with answer will be the course in degrees and minutes. 

If the index number for Tangent is 8 or 9 the course mil 
be from top of page. 

If the index mmiber for Tangent is 10 or 11 the course will 
be from bottom of page. 

Take out the Logarithm Secant from Table 44 for the 
degrees and minutes of the course, rejecting the 10 from the 
index number. 

Take out the logarithm of difference of latitude (Table 
42) applying its index number by rule above. 

Add together Logarithm Secant of coiu-se, and logarithm 
of difference of latitude. 

The logarithm that agrees with this sum in the body of 
the logarithms, Table 42, will be the distance in the left- 
hand column for the first 3 numbers, and the number of the 
column logarithm was found in on top will be the last 
number. 

If the index number is 1 the distance will be in 2 figures. 
If the index number is 2 the distance will be in 3 figures. 
If the index number is 3 the distance will be in 4 figures. 

PROBLEM NO. 1 

Lat. A 43^ 08' N Mer Parts 2858.0 Long. A 5° 56' E 
Lat. B 39° 29' N Mer Parts 2567.5 Long. B 0° 24' W 



3° 39' 290.5 6° 20' 

60 60 



180 360 

4-39 +20 



D. L. 219 Diff. Lon. 380 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 107 

Log. of Diff . Long. 380 = 12 . 57978 

Log. of Mer. Parts 290 . 5 = 2 . 46315 



Tangent 10 . 11663 = Course S 52^36' W 



Secant of Course 52° 36'= 0.21654 
Log of Diff. Lat. 219 = 2 . 34044 



Log. 2.55698 =Dist. 360.6 miles 



PROBLEM NO. 2 

Lat. A 15° 55' S Mer. Parts 961 . 1 Long. A 5° 44' W 
Lat. B 55° 59' S Mer. Parts 4052.7 Long. B 67° 16' W 



Diff. Lat. 2404' Mer. Parts 3091.6 Diff. Long. 3692' 

Log. of Diff. Long. 3692 = 13 . 56726 
Log. of Mer. Parts 3092 = 3.49024 



Tangent 10 . 07702 = Course S 50° 03' W 



Secant of Course 50° 03' =0.19238 
Log of Diff. Lat. 2404 = 3 . 38093 



Log. 3 . 57331 = Dist. 3744 miles 



PROBLEM NO. 3 



Lat. A 15° 12' S Mer. Parts 916.8 Long. A 2° 12' E 
Lat. B 28° 49' S Mer. Parts 1795.6 Long. B 17° 11' E 



Diff. Lat. 817' S Mer. Parts 878.8 Diff. Long. 899' 

Log. of Diff. Long. 899 = 12 . 95376 
Log. of Mer. Parts 878 . 8 = 2 . 94389 



Tangent 10 . 00987 = Course S 45° 39' E 



Secant of Course 45° 39' = . 15550 
Log. of Diff. Lat. 817' = 2 . 91222 



Log. 3 . 06772 = Dist. 1 169 miles 



108 SIMPLE RULES AND PROBLEMS IN NAVIGATION 
PROBLEM NO. 4 

Lat. A 17° 15' S Mer. Parts 1044.1 Long. A 92° 21' W 
Lat. B 31° 42' S Mer. Parts 1994.9 Long. B 110° 10' W 



Diff. Lat. 867' Mer. Parts 950.8 Diff. Long. 1069' 

Log. of Diff. Long. 1069 = 13 . 02898 
Log. of Mer Parts 950 . 8 = 2 . 97809 



Tangent 10, 05089 = Course S 48° 21' W 



Secant of Course 48° 21' = . 17745 
Log. of Diff. Lat. 867 = 2 . 93802 



Log. 3 . 1 1547 = Dist. 1305 miles 



PROBLEM NO. 5 



Lat. A 18° 12' S Mer. Parts 1103.5 Long. A 18° 10' E 
Lat. B 46° 11' S Mer. Parts 3114.5 Long. B 32° 21' W 



Diff. Lat. 1679' Mer. Parts 2011 Diff. Long. 3031' 

Log. of Diff. Long. 3031 = 13 . 48159 
Log. of Mer. Parts 2011 = 3.30341 

Tangent 10 . 17818 = Course S 56' 26' W 

Secant of Course 56° 26'= 0.25735 
Log. of Diff. Lat. 1679 = 3 . 22505 

Log. 3 . 48240 = Dist. 3037 miles 



PROBLEM NO. 6 

Lat. A 30° 29' N Mer. Parts 1910. 1 Long. A 179° 47' E 
Lat. B 15° 12' N Mer. Parts 916.8 Long. B 126° 44' E 



Diff. Lat. 917' Mer. Parts 993.3 Diff. Long. 3183' 

Log. of Diff. Long. 3183 = 13 . 50284 
Log. of Mer .Parts 993 . 3 = 2 . 99708 

Tangent 10 . 50576 = Course S 72° 40' W 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 109 

Secant of Course 72° 40'= 0.52589 
Log. of Diff. Lat 917 = 2 . 96237 



Log. 3 . 48826 = Dist. 3078 miles 



PROBLEM NO. 7 



Lat. A 8^ 05' S Mer. Parts 483.3 Long. A 18° 02' W 
Lat. B 62° 04' S Mer. Parts 4762.8 Long. B 103° 03' W 



Diff. Lat. 3239' Mer. Parts 4279.5 Diff. Long. 5101' 

Log. of Diff. Long. 5101 = 13 . 70766 
Log. of Mer. Parts 4279 = 3 . 63134 



Tangent 10 . 07632 = Course S 50° 01 ' W 

Secant of Course 50° 01' = . 19208 
Log. of Diff. Lat 3239 = 3 . 51041 



Log. 3 . 70249 = Dist. 5041 miles 



PROBLEM NO. 8 



Lat. A 0° 00' Mer. Parts 0000.0 Long. A 0° 02' W^ 
Lat. B 51° 12' N Mer. Parts 3569.7 Long. B 16° 14' E 



Diff. Lat. 3072' Mer. Parts 3569.7 Diff. Long. 976' 

Log. of Diff. Long. 976 = 12 . 98945 
Log. of Mer. Parts 3570 = 3 . 55267 

Tangent 9 . 43678 = Course N 15° 17' E 

Secant of Course 15° 17'= 0.01564 
Log. of Diff. Lat. 3072= 3.48742 

Log. 3 . 50306 = Dist. 3185 miles 



PROBLEM NO. 9 

Lat. A 71° 02' S Mer. Parts 6129.7 Long. A 16° 12' E 
Lat. B 22° 05' S Mer. Parts 1350.3 Long. B 102° 15' E 



Diff, Lat. 2937' Mer. Parts 4779 Diff. Long. 5163' 



110 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

Log. of Diff. Long. 5163 = 13 . 71290 
Log. of Mer. Parts 4779 = 3 . 67934 

Tangent 10 . 03356 = Course N 47° 13' E 

Secant of Course 47° 13'= 0.16798 
Log. of Diff. Lat. 2937= 3.46790 



Log. 3 . 63588 = Dist. 4324 miles 



PROBLEM NO. 10 

Lat. A 14° 12' S Mer. Parts 855.1 Long. A 178° 02' E 
Lat. B 79° 02' S Mer. Parts 8033.2 Long. B 115° 16' W 



Diff. Lat. 3890' Mer. Parts 7178 . 1 Diff. Long. 4002' 

Log. of Diff. Long. 4002 = 13 . 60228 
Log. of Mer. Parts 7178 = 3 . 85600 

Tangent 9 . 74628 = Course S 29° 08' E 

Secant of Course 29° 08' = . 05877 
Log. of Diff. Lat. 3890 = 3 . 58995 



Log. 3 . 64872 = Dist. 4454 miles 



PROBLEM NO. 11 



Lat. A 3° 12' N Mer. Parts 190.8 Long. A 118° 00' W 
Lat. B 79° 15' N Mer. Parts 8102.2 Long. B 142° 12' W 



Diff. Lat. 4563' Mer. Parts 7911 Diff. Long. 1452' 

Log. of Diff. Long 1452 = 13 . 16197 
Log. of Mer. Parts 7911 = 3.89823 



Tangent = 9 . 26374 = Course N 10° 24' W 



Secant of Course 10° 24'= 0.00719 
Log. of Diff. Lat 4563 = 3 . 65925 



Log. 3 . 66644 = Dist. 4639 miles 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 111 

PROBLEM NO. 12 

Lat. A 19° 36' N Mer. Parts 1191.8 Long. A 18° 12' E 
Lat. B 21° 42' S Mer. Parts 1325.6 Long. B 2° 06' W 



Diff. Lat. 2478' Mer. Parts 2517 Diff. Long. 1218' 

Log. of Diff. Long. 1218 = 13 . 08565 
Log. of Mer. Parts 2517 = 3.40088 

Tangent 9 . 68477 = Course S 25° 49' W 

Secant of Course 25° 49'= 0.04566 
Log. of Diff. Lat. 2478 = 3 . 39410 



Log. 3 . 43976 = Dist. 2753 miles 



PROBLEM NO. 13 



Lat. A 36° 08' N Mer. Parts 2314.1 Long. A 159° 00' E 
Lat. B 17° 17' S Mer. Parts 1046.1 Long. B 159° OO'W 



Diff. Lat. 3205' Mer. Parts 3360 Diff, Long. 2520' 

Log. of Diff. Long. 2520 = 13 . 40140 
Log. of Mer. Parts 3360 = 3 . 52634 

Tangent 9 . 87506 = Course S 36° 52' E 

Secant of Course 36° 52'= 0.09689 
Log. of Diff. Lat. 3205 = 3 . 50583 



Log, 3 . 60272 = Dist. 4006 miles 



PROBLEM NO. 14 



Lat. A 9° 18' S Mer. Parts 556.7 Long. A 74° 13'^ E 
Lat. B 42° 17' S Mer. Parts 2788.9 Long. B 47° 17' E 



Diff. Lat. 1979' Mer. Parts 2232.2 Diff. Long. 1616' 

Log. of Diff. Long. 1616 = 13 . 20844 
Log. of Mer. Parts 2232= 3.34869 



Tangent 9 . 85975 = Course S 35° 54' W 



112 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

Secant of Course 35° 54'= 0.09149 
Log. of Diff. Lat. 1979 = 3.29645 



Log. 3 . 38794 = Dist. 2443 miles 



PROBLEM NO. 15 



Lat. A 14° 06' N Mer. Parts 849.0 Long. A 81° 59' W 
Lat. B 32° 55' N Mer. Parts 2080.8 Long. N 59° 17' W 



Diff. Lat. 1129' Mer. Parts 1232 Diff. Long. 1362' 

Log. of Diff. Long. 1362 = 13 . 13418 
Log. of Mer. Parts 1232 = 3 . 09061 



Tangent 10 . 04357 = Course N 47° 52' E 

Secant of Course 47° 52' = . 17337 
Log. of Diff. Lat. 1129= 3.05269 



Log. 3 . 22606 = Dist. 1683 miles 



PROBLEM NO. 16 



Lat. A 0° 06' N Mer. Parts 6.0 Long. A 0° 00' W 
Lat. B 60° 10' N Mer. Parts 4527.1 Long. B 41° 02' W 



Diff. Lat. 3604' Mer. Parts 4521 Diff. Long. 2462' 

Log. of Diff. Long. 2462 = 13 . 39129 
Log. of Mer. Parts 4521 = 3.65523 

Tangent 9 . 73606 = Course N 28° 34' W 

Secant of Course 28° 34'= 0.05638 
Log. of Diff. Lat. 3604 = 3 . 55678 



Log. 3 . 61316 = Dist. 4103 miles 



PROBLEM NO. 17 



Lat. A 34° 22' S Mer. Parts 2184.9 Long. A 18° 24' E 
Lat. B 15° 55' S Mer. Parts 961.1 Long. B 5° 45' W 



Diff. Lat. 1107' Mer. Parts 1224 Diff. Long. 1449' 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 113 

Log. of Diff. Long. 1449 = 13 . 16107 
Log. of Mer. Parts 1224 = 3 . 08778 

Tangent 10 . 07329 = Course N 49° 49' W 

Secant of Course 49° 49' = . 19028 
Log. of Diff. Lat. 1107 = 3 . 04415 



Log. 3 . 23443 = Dist. 1716 miles 



PROBLEM NO. 18 



Lat. A 8° 04' S Mer. Parts 482.3 Long. A 34° 53' W 
Lat. B 14° 45' N Mer. Parts 889.0 Long. B 17° 32' W 



Diff. Lat. 1369' Mer. Parts 1371 Diff. Long, 1041' 

Log. of Diff. Long. 1041 = 13 . 01745 
Log. of Mer. Parts 1371= 3.13704 

Tangent 9 . 88041 = Course N 37° 12' E 

Secant of Course 37° 12'= 0.09880 
Log. of Diff. Lat. 1369= 3.13640 



Log. 3 . 23520 = Dist. 1719 miles 



CHAPTER VI 
MIDDLE LATITUDE SAILING 

This method is to find the course and distance between 
two places, when the distance is small. 

Proceed as in Mercators sailing to find the difference of 
latitude and longitude in minutes. 

Find the Middle Latitude between the places as in Day's 
Work. 

Take the Middle Latitude to the nearest degree as a 
course, and in Table 2 (Bowditch) look in the Distance 
column for the difference of longitude in minutes, and in the 
latitude colunan corresponding to this distance will be the 
Departure in miles. 

Compare the difference of latitude in miles and departm-e 
in miles in Ta,ble 2, and the course and distance will be found 
as in Day's Work. 

Never cross the equator with this method. 

PROBLEM NO. 1 

Lat. A 28° 17' N 28° 17' Long. A 14° 16' W 

Lat. B 30° 02' N 30° 02' Long. B 23° 10' W 



1° 45' 58° 19' 8° 54' 

Diff. Lat. 105' 29° 09' Mid. Lat. 

or 105 miles Diff. Long. 534' 

Departure 467 miles 
Course N 77° W. Distance 479 miles. 

PROBLEM NO. 2 

Lat. A 38° 16' S 38° 16' Long. A 102° 12' E 

Lat. B 40° 12' S 40° 12' Long. B 108° 11' E 



1° 56' 78° 28' 5° 59' 

Diff. Lat. 116' 39° 14' Mid. Lat. 

or 116 miles Diff. Long. 359' 

Departure 279.0 miles 
Course S 67° E. Distance 302 miles. 

114 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 115 



PROBLEM NO. 3 



Lat. A 76° 08' S 
Lat. B 74° 16' S 



76° 08' 
74° 16' 



Long. A 179° 53' E 
Long. B 178° 10' W 



1° 52' 
Diff. Lat. 112' 
or 112 miles 



1° 57' 



150° 24' 
75° 12' Mid Lat 

Diff. Long. 117' 
Departure 30 . 3 miles 



Course N 15° E. Distance 116 miles. 



PROBLEM NO. 4 



Lat. A 42° 08' N 
Lat. B 47° 05' N 



42° 08' 
47° 05' 



Long. A 18° 23' E 
Long. B 21° 06' E 



4° 57' 
Diff. Lat. 297' 
or 297 miles 



2° 43' 



89° 13' 

44° 36' Mid Lat. 

Diff. Long. 163' 
Departure 115.3 miles 



Course N 21° E. Distance 318 miles. 



PROBLEM NO. 5 



Lat. A 51° 53' N 
Lat. B 56° 18' N 



51° 53' 
56° 18' 



Long. A 37° 18' W 
Long. B 40° 17' W 



4° 25' 
Diff. Lat. 265' 
or 265 miles 



2° 59' 



108° 11' 
54° 05' Mid. Lat. 

Diff. Long. 179' 
Departure 105 . 2 miles 



Course N 22° W. Distance 285 miles. 



Lat. A 43° 10' S 
Lat. B 40° 08' S 



3° 02' 
Diff. Lat. 182' 
or 182 miles 



PROBLEM NO. 6 



43° 10' 
40° 08' 



Long. A 108° 00' W 
Long. B 109° 40' W 



1° 40' 



83° 18' 

41° 39' Mid. Lat. 

Diff. Long. 100' 
Departure 74 . 3 miles 



Course N 22° W. Distance 197 miles. 



116 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



Lat. A 12° 13' S 
Lat. B 9° 16' S 


PROBLEM NO. 7 

12° 13' Long. A 14° 18' E 
9° 16' Long. B 17° 03' E 


2° 57' 
Diff. Lat. 177' 


21° 29' 2° 45' 
10° 44' Mid. Lat. 

Diff. Long. 165' 
Departure 162.0 miles 



True course N 42° E. Distance 240 miles. 



PROBLEM NO. 8 

Lat. A 49° 06' N 49° 06' Long. A 179° 15' E 

Lat. B 51° 10' N 51° 10' Long. B 179° 32' W 



2° 04' 100° 16' 1° 13' 

Diff. Lat. 124' 50° 08' Mid. Lat. 

Diff. Long. 73' 
Departure 46.9 miles 

Course N 21° E. Distance 133 miles. 
PROBLEM NO. 9 



mt. A 38° 07' N 
Lat. B 36° 51' N 


38° 07' Long. A 
36° 51' Long. B 


13° 12' E 
19° 06' E 


1° 16' 
Diff. Lat. 76' 


74° 58' 5° 54' 
37° 29' Mid. Lat. 

Diff. Long. 354' 
Departure 282 . 7 miles 


Course S 75° E. 


Distance 292 miles. 
PROBLEM NO. 10 




Lat. A 14° 28' S 
T-R,t. B 10° 19' S 


14° 28' Long. A 
10° 19' Long. B 


0° 06' W 

7° 18' E 


4° 09' 
Diff. Lat. 249' 


24° 47' 7° 24' 
12° 23' Mid. Lat. 

Diff. Long. 444' 
Departure 434.3 miles 



Course N 60° E. Distance 500 miles. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 117 

PROBLEM NO. 11 

Lat. A 6° 14' N 6° 14' Long. A 28° 13' E 

Lat. B 14° 16' N 14° 16' Long. B 26° 09' E 



8° 02' 20° 30' 2° 04' 
Diff. Lat. 482' 10° 15' Mid. Lat. 

Diff. Long. 124' 
Departure 122 . 1 miles 


Course N 14° W. Distance 497 miles. 




PROBLEM NO. 12 




Lat. A 60° 10' N 60° 10' Long. A 
Lat. B 58° 11' N 58° 11' Long. B 


4° 16' W 
6° 18' W 


1° 59' 118° 21' 
Diff. Lat. 119' 59° 10' Mid. Lat. 


2° 2' 



Diff. Long. 122' 
Departure 62 . 8 miles 

Course S 28° W. Distance 135 miles. 



CHAPTER VII 
LATITUDE BY MERIDIAN ALTITUDE OF SUN 

The latitude by the sun is found most easily by a noon 
sight, when the sun is on the meridian, or the highest point 
reached by the sun on that day. 

When the sun crosses the meridian it is either directly 
overhead or due north or south. It is then exactly Oh 00' 
00'' local apparent time. 

A chronometer always shows Greenwich time, and if we 
could read the chronometer when the sun was exactly at its 
highest point and was about to descend, we could use that 
time to look up the declination in the Nautical Almanac. 

As at this time the sun's motion is nearly horizontal, i.e., 
its rise is very slow, it is very difficult to tell when it has 
ceased to ascend and is starting to descend. 

If the longitude is known, the Greenwich apparent time 
may be found; for longitude expressed in hours, minutes and 
seconds is the difference between local and Greenwich time. 

If in west longitude the apparent time at Greenwich will 
be past noon : therefore, add the longitude in time to hours, 
and the answer will be the G. A. T. on the same day as the 
ship. 

If in east longitude the apparent time at Greenwich will 
be before noon; therefore, subtract the longitude in time 
from 24 hours and the answer will be the G. A. T. of the 
day before. 

In the Nautical Almanac, the equation of time is given 
with + or — signs to show whether it is to be added to or 
subtracted from the G. M. T. to get the G. A. T. 

Since the G. A. T. is known and the G. M. T. is desired, 
the equation of time is applied the opposite way to that 
shown by the signs in the Nautical Almanac. 

It is necessary to know the G. M. T. when the sight 
was taken for the declination at that instant must be known 
and the declination is given in the Nautical Almanac for 
G. M. T. and not for G. A. T. or L. A. T. 

118 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 119 

The declination of the sun is the distance north or south 
of the equator. The sign + in the almanac means north, 
the sign -south. The declination is given for each day and 
on the even hour of that day. 

To find the declination for any given time, look up in the 
almanac the declination for the even hour preceding. This is 
corrected by adding or subtracting the change in the inter- 
vening minutes. The hourly difference (H. D.) is found 
printed in the almanac at the end of each day. This is mul- 
tiplied by the fractional part of an hour to get the correction. 
If the declination is decreasing this is subtracted, if increas- 
ing it is added. 

The altitude is measured by the sextant. 

When the sun is on the meridian, it is either due north, 
directly overhead, or due south of the observer. 

The index error (I. E.) is the error of the sextant used for 
the observation. When it is " off the scale '^ it is added; 
when ^' on scale 'Mt is subtracted. 

The semi-diameter (S. D.) is half the diameter of the sun, 
or the distance from the bottom or top of the sun to the 
center. In lower limb (L. L.) sights, or sights taken on the 
lower edge, the S. D. is added. In upper limb (U. L.) 
signts it is subtracted. It is given in the Nautical Almanac. 
The nearest date is used and the nearest .1 of a minute. 

The dip correction is the correction for the height of the 
eye of the observer above sea level. It is always subtracted 
and is found in Table 14 (Bowditch). 

Refraction is the change of direction of a ray of light in 
passing through the atmosphere. 

Parallax is the error caused by taking altitude from the 
surface of the earth while the calculations are made on the 
assumption that the observer is at the center of the earth. 

The corrections for refraction and parallax (R. & P.) are 
combined in Table 20B and are always subtracted. 

After making these corrections to the observed meridian 
altitude, the answer is the true altitude. 

The point in the sky directly over the observer's head is 
the zenith. It is 90° from the horizon in all directions. 

Subtracting the altitude from 90° gives the zenith dis- 
tance (Z. D.) or distance from the sun to the zenith. It 
always has the opposite name to the sun's bearing. 

Under zenith distance put down the declination. 

If both are the same name add : the sum is the latitude, 
named the same. 



120 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

If different names, subtract the lesser from the greater; 
the difference is the latitude, named the same as the greater. 

PROBLEM NO. 1 

Jan. 30, 1919. Obs. Mer. Alt. Sun's L. L. 44° 18' S. Dip 36 ft. 
Long. 91° W. 



Longitude ii 
Obs. Alt 


1 time 6h 04'. 

44° 18' 00" 

+ 16' 18" 


N 
S 


L. A. T., 30d 

Long. 

G. A. T. 

Eq. Time 

G. M. T., 30d 
30d 

Dec. for 30 d 6li 

Corr. for .3h 

Dec.for30d6.3h 


Oh 00' 00" 
+ 6h 04' 00" 


S. D. 


6h 04' 00" 




44° 34' 18" 
5' 53" 


+ 13' 22" 


Dip 


6h 17' 22" or 


R.&P. 


44° 28' 25" 
53" 


6.3h 


True Alt. 
True Alt. 


44° 27' 32" 

90° 00' 00" 
44° 27' 32" 


17° 47'.9 S 
- .2 


Z. D. 
Dec. 


45° 32' 28" 
17° 47' 42" 


17° 47'.7 P 



Lat. 27° 44' 46" N D. for .3h = .3X.7'=.2' 

PROBLEM NO. 2 

Feb. 1, 1919. Obs. Mer. Alt. Sun's L. L. 78° 05' 05" S. Dip 12 ft. 
Long. 78° 14' E. 

Longitude in time 5 h 12' 56" L. A. T., Feb., Id Oh 00' 00" 

Obs. Alt. 78° 05' 05" ^^"^^ '^ ^^' '^" 

S. D. + 16' 18" G. A. T., Jan. 31 18h 47' 04" 

Eq. Time + 13' 36" 

Dip - 3' 24" Q, M. T., Jan. 31 19h 00' 40" 



78° 


21' 


23" 




3' 


24" 


78° 


17' 


59" 
10" 



R.&P. 

True Alt. 78° 17' 49' 

90° 00' 00' 

True Alt. 78° 17' 49' 



Z. D. 11° 42' 11" N Dec. for 31d 18h 17° 23'.1 S 

Dec. 17° 22' 24" S H. D. - .7 dec. 



Lat. 5° 40' 13" S Dec. for 31d 19h 17° 22'.4 S 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 121 



PROBLEM NO. 3 

Mar. 20, 1919. Obs. Mer. Alt. Sun's L. L. 89** 37' N. Index Error 
+4' 27". Dip 18 ft. Long. 111° E. 

Longitude in time 7h 24'. L. A. T., 20d Oh 00' 00" 

„ ^ Long. 7h 24' 00" 

Obs. Alt. 89° 37' 00" ^ 



I. E. + 4' 27" G. A. T., 19d 16h 36' 00' 

Eq. Time + 7' 55' 



89° 


41' 
16' 


27" 
06" 


89° 


57' 
4' 


33" 
09" 


89° 


53' 


24" 
00" 



S. D. + 16 06 G. M. T. 16h 43' 55" 

19d 16.7h 

89° 57' 33" 

Dip 

R.&P. 

89° 53' 24" 

Z. D. 0° 06' 36" S Dec. for 19d 16h 0** 35'.9 S 

Dec. 0° 35' 12" S Corr. for .7h - 0'.7 



-or 



Lat. 0° 41' 48" S Dec. for 19d 16.7h 0° 35'.2 S 



PROBLEM NO. 4 

Mar. 10, 1919. Obs. Mer. Alt. Sun's L. L. 59° 59' 50" S. Index Error 
+50". Dip 15 ft. Long. 102° 41' W. 



Longitude in 
Obs. Alt. 


time 6h 50' 44". 

59° 59' 50" 
+ 50" 


L. A. T., lOd 

Long. 

G. A. T. 
Eq. Time 

G. M. T. 

lOd 

Dec. for lOd 6h 
Corr. for 1 h 

Dec. for lOd 7h 


Oh 00' 00" 
6h 50' 44" 


LE. 


6h 50' 44" 




60° 00' 40" 
+ 16' 06" 


+ 10' 35" 


S.D. 


7h or 19" or 


Dip 


60° 16' 46" 
3' 48" 


7h 


R.&P. 


60° 12' 58" 
30" 




Z. D. 
Dec. 


60° 12' 28" 

29° 47' 32" N 
4° 17' 24" S 


4° 18'.4 S 
I'.O 


Lat. 


25° 30' 08" N 


4° 17'.4 S 



122 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 5 

Jan. 31, 1919. Obs. Mer. Alt. Sun's L. L. 46° 56' S. Dip 36 ft. 

Long. 94° W. 



Longitude in 
Obs. Alt. 


time 6h 16'. 

46° 56' 00" 
+ 16' 18" 


N 
S 

N 


L. A. T., 31d 

Long. 

G. A. T. 
Eq. Time 

G. M. T. 

Sid 

Dec. for 31d 6h 
Corr. for .5h 

Dec. for 31d 6.5h 


Oh 00' 00" 

+ 6h 16' 00" 


S. D. 


6h 16' 00" 




47° 12' 18" 
5' 53" 


+ 13' 31" 


Dip 


6h 29' 31" or 


R.&P. 


47° 06' 25" 

- 48" 


6.5h 


True Alt. 

Z.D. 
Dec. 


47° 05' 37" 

42° 54' 23" 
17° 31' 06" 


17° 31'.4 S 
0'.3 dec. 


Lat. 


25° 23' 17" 


17° 31'.1 S 



PROBLEM NO. 6 

Mar. 21, 1919. Obs. Mer. Alt. Sun's L. L. 57° 21' S. Dip 38 ft. 
Long. 77° 26' W. 

Longitude in time 5h 09' 44" L. A. T., 21d Oh 00' 00" 

Obs. Alt. 57° 21' 00" ^°"^- +5h09'44" 



S. D. 


+ 16' 06" 


N 
N 


G. A. T. 

Eq. Time 

G. M. T. 

21d 

Dec. for 21d 4h 
Corr. for 1.3h 


+ 


5h 09' 44" 




57° 37' 06" 
- 6' 02" 


7' 28" 


Dip 


5h 17' 12" or 


R.«&P. 


57° 31' 04" 
0' 32" 


5.3h 


True Alt. 

Z.D. 
Dec. 


57° 30' 32" 

32° 29' 28" 
01' 00" 


0° 00'.3 S 
01'.3 



Lat. 32° 30' 28" N Dec= for 21d 5.3h. 0° Ol'.O N 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 123 



PROBLEM NO.x7 

Sept. 3, 1919. Obs. Mer. Alt. Sun's L. L. 49° 02' 15" S. Dip 28 ft. 
Long. 118° 15' E. 



Longitude in 
Obs. Alt. 


time 7h 53' 

49° 02' 15" 
+ 15' 54" 


S 

S 

N 
N 


L. A. T., 3d 

Long. 

G. A. T., 2d 
Eq. Time 

G. M. T., 2d 
2d 

Dec. for 2d 16h 
Corr. for .Ih 


Oh 00' 00" 
- 7h 53' 00" 


S.D. 


16h 07' 00" 




49° 18' 09" 
- 5' 11" 


- 0' 18" 


Dip. 


16h 06' 42" or 


R. &P. 


49° 12' 58" 
- 45" 


16. Ih 


True Alt. 


49° 12' 13" 
90° 00' 00" 




Z. D. 
Dec. 


40° 47' 47" 
7° 58' 06" 


7° 58'.2 N 
O'.l 



Lat. 48° 45' 53" N Dec. 2d 16.1h 7° 58'.1 N 



PROBLEM NO. 8 

Aug. 8, 1919. Obs. Mer. Alt. Sun's L. L. 38° 16' N. Dip 27 ft. 
Long. 3° 15' W. 



Longitude ii 
Obs. Alt. 


1 time Oh 13' 

38° 16' 00" N 
+ 15' 48" 


G. A. T., 8d 

Eq. Time 

G. M. T., 8d 
8d 

Dec, 8d Oh. 
Corr., for .3h 


Oh 13' 00" 
+ 5' 37" 


S.D. 


Oh 18' 37" or 


Dip 


38° 31' 48" 
5' 06" 


0.3h 


R.&P. 


38° 26' 42" 
- V 07" 




True Alt. 


38° 25' 35" 
90° 00' 00" 




Z. D. 
Dec. 


61° 34' 25" S 
16° 22' 24" N 


16° 22.'6 N 
0'.2 



Lat. 35° 12' 01" S Dec. 8d 0.3h 16° 22'.4 N 



124 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 9 

July 4, 1919. Obs. Mer. Alt. Sun's L. L. 70° 15' S. Dip 24 ft. 
Long. 97° 12' W. 

Longitude in time 6h 28' 48". L. A. T., 4d Oh 00' 00" 

Obs. Alt. 70° 15' 00" ^^^^- H_6h28M8" 



S- -D- + 15' 48" Q A. T. 6h 28' 48' 

Eq. Time + 4' 04' 



70° 30' 48' 



I^iP ^' '^^" G. M. T.,4d 6h 32' 52" or 

70° 26' 00" 
R. & P. - 18" 



70° 25' 42" 



Z. D. 19° 34' 18" N Dec. for 4d 6h 22° 56'.0 N 

Dec. 22° 55' 54" N Corr. for .5h - O'.l 



Lat. 42° 30' 12" N Dec. for 4d 6.5h 22° 55'.9 N 



PROBLEM NO. 10 

Apr. 18, 1919. Obs. Mer. Alt. Sun's L. L. 41° 02' S. Dip 22 ft. 
Long. 97° 15' E. 



Longitude in 
Obs. Alt. 


time 6h 29' 00". 

41° 02' 00" 
+ 16' 00" 


L. A. T., 18d 

Long. 

G. A. T., 17d 

Eq. Time 

G. M. T., 17d 
17d 

Dec. for 17d, 1( 
Corr. for 1.5h 


Oh 00' 00" 
6h 29' 00" 


S. D. 


17h 31' 00" 




41° 


18' 00" 
4' 36" 


- 0' 25" 


Dip 


17h 30' 35" or 


R.&P. 


41° 


13' 24" 
59" 


17.5h 


Z. D. 
Dec. 


41° 

48° 
10° 


12' 25" 

47' 35" N 

27' 18" N 


3h +10° 26'.0 N 
+ 1'.3 



Lat. 59° 14' 53" N Dec. for 17d 17.5h 10° 27'.3 N 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 125 



PROBLEM NO. 11 

Mar. 11, 1919. Obs. Mer. Alt. Sun's L. L. 81° 16' N. Index Error 
-3' 20". Dip 28 ft. Long. 19° 16' E. 



Longitude in 
Obs. Alt. 


time Ih 17' 04" 

81° 16' 00' 
3' 20" 


S 

s 
s 


L. A. T., lid 

Long. 

G. A. T., lOd 

Eq. Time 

G. M. T. 

lOd 

Dec. for lOd 22h 
Corr. for .9h 

Dec.forl0d22.9h 


Oh 00' 00"' 
Ih 17' 04" 


I.E. 


22h 42' 56" 




81° 12' 40" 
+ 16' 06" 


+ 10' 23" 


S.D. 


22h 53' 19" or 


Dip 


81° 28' 46'' 
5' 11" 


22.9h 


R. &P. 


81° 23' 35" 
07" 




True Alt. 

Z. D. 
Dec. 


81° 23' 28" 

8° 36' 32" 
4° 01' 54" 


4° 02'.8 S 
0'.9 


Lat. 


12° 38' 26" 


4° 01'.9 S 



PROBLEM NO. 12 

Oct. 23, 1919. Obs. Mer. Alt. Sun's L. L. 37° 21' S. Index Error 
4-9' 10". Dip 16 ft. Long. 86° 15' W. 



Longitude i] 
Obs. Alt. 


a time 5h 45' 

37° 21' 00" 
+ 9' 10" 


L. A. T., 
Long. 

G. A. T. 
Eq. Time 

G. M. T. 


23d 
23d 


Oh 00' 00" 
5h 45' 00" 


LE. 


5h 45' 00" 




37° 30' 10" 

+ 16' 06" 


— 15' 31" 


S.D. 


5h 29' 29" or 




m-rO Am -t rt 1 1 


5.5h 



37° 46' 16" 
Dip ~ 3' 55' 



37° 42' 21' 
R. & P. - 1' 08' 



True Alt. 37° 41' 13" 

Z. D. 52° 18' 47" N Dec. for 23d 4h 11° 11' .6 S 

Dec. 11° 12' 54" S Corr. for 1.5h + 1' .3 



Lat. 41° 05' 53" N Dec. for 23d 5.5h 11° 12' .9 S 



126 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 13 

Oct. 11, 1919. Obs. Mer. Alt. Sun's L. L. 26° 53' 10" S. Index Error 
-2' 40". Dip 17 ft. Long. 18° 02' W. 



Longitude in 
Obs. Alt. 


time Ih 12' 08" 

26° 53' 10" S 

2' 40" 


G. A. T., lid 

Eq. Time 

G. M. T., lid 
lid 

Dec. for lid Oh 
Corr. for Ih 


Ih 12' 08" 
13' 00" 


LE. 


Oh 59' 08" or 


S.D. 
Dip 


26° 50' 30" 
+ 16' 03" 

27° 06' 33" 
- 4' 02" 


Ih 


R.i&P. 


27° 02' 31" 
r 46" 




True Alt. 


27° 00' 45" 
90° 00' 00" 




Z.D. 
Dec. 


62° 59' 15" N 
6° 44' 30" S 


6° 43'.6 S 
+ 0.9 



Lat. 56° 14' 45" N Dec. lid Ih 6° 44'.5 S 



PROBLEM NO. 14 

Apr. 3, 1919. Obs. Mer. Alt. Sun's L. L. 60° 22' S. Dip 21 ft. 
Long. 20° 59' E. 



Longitude in 
Obs. Alt. 


time Ih 23' 56" 

60° 22' 00" 
4- 16' 00" 


S 

S 

N 
N 


L. A. T., 3d 
Long. 

G. A. T., 2d 

Eq. T. 

G. M. T., 2d 
2d 

Dec. for 2d 22h 
Corr. .7h 


OOh 00' 00" 
- Ih 23' 56" 


S.D. 


22h 36' 04" 




60' 38" 00" 
- 4' 29" 


+ 3' 36" 


Dip 


22h 39' 40" or 


R. & P 


60° 33' 31" 

0' 28" 


22.7h 


True Alt. 

Z.D. 
Dec. 


60° 33' 03" 

29° 26' 57" 
4° 59' 30" 


4° 58.'8 N 
4- 0'.7 



Lat. 34° 26' 27" N Dec. 2d 22.7h 4° 59'.5 N 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 127 



PROBLM NO. 15 

Aug. 30, 1919. Obs. Mer. Alt. Sun's L. L. 57° 18' 30" N. Index Error 
+45". Dip 18 ft. Long. 129° 15' W. 

Longitude in time 8h 37' G. A. T., 30d 8h 37' 00" 

Obs. Alt. 57° 18' 30" N ^^- ^^"^ + ^" 

LE. 

S.D. 

Dip 



+ 45" 


G. M. T., 30d 
30d 

Dec. for 30d 8h 

Corr. .6h 


8 37' 44" or 


57° 19' 15" 
+ 15' 54" 


8.6h 


57° 35' 09" 
- 4' 09" 




57° 31' 00" 
32" 




57° 30' 28" N 

32° 29' 32" S 
9° 09' 54" N 


9° 10'.4 N 
0'.5 



R.&P. 

True Alt. 

Z. D. 
Dec. 

Lat. 23° 19' 38" S Dec. 30d 8.6h 9° 09'.9 N 



PROBLEM NO. 16 

Dec. 3, 1919. Obs. Mer. Alt. Sun's L. L. 64° 45' 15" N. Index Error 
-1' 10". Dip 20 ft. Long. 63° 18' E. 



Longitude in 
Obs. Alt. 


time 4h 13' 12". 

64° 45' 15" 
1' 10" 


N 

N 

S 
S 

S 


L. A. T., 3d 

Long. 

G. A. T., 2d 

Eq. Time 

G. M. T., 2d 
2d 

Dec. for 2d 18h 
Corr. 1.6h 

Dec. 


OOh 00' 00" 
- 4h 13' 12" 


LE. 


19h 46' 48" 




64° 44' 05" 
+ 16' 18" 


- 10' 30" 


S.D. 


19h 36' 18" or 


Dip 


65° 00' 23" 
4' 23" 


19.6h 


R.&P. 


64° 56' 00" 
23" 




True Alt. 

Z.D. 
Dec. 


64° 55' 37" 

25° 04' 23" 

21° 58' 18" 


21° 57'.7 S 
+ 0'.6 


Lat. 


47° 02' 41" 


21° 58'.3 S 



128 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 17 

Mar. 20, 1919. Obs. Mer. Alt. Sun's L. L. 89° 42' 40" N. Index Error 
4-2' 20". Dip 20 ft. Long. 101° 30' W. 

Long, in time 6h 46' L. A. T., 20d Oh 00' 00" 

Obs. Alt. 89»42'40" ^°"^- + 6h 46' 00" 



LC. 


+ 2' 20" 


G. A. T. 
Eq. Time 

G. M. T. 

20d 

Dec.for20d6h 
Corr. for .9h 


+ 


6h 46' 00" 




89° 45' 00" 
16' 06" 


7' 45" 


S.D. 


6h 53' 45" or 


Dip 


90° 01' 06" 
4' 23" 


6.9h 


True Alt. 

Z.D. 
Dec. 


89° 56' 43" 

3' 17" S 
21' 06" S 


0° 22'.0 S 
0'.9 



Lat. 0° 24' 23" S Dec. for 20d 6.9h 0° 21'.1 S 



LATITUDE CONSTANT 

In practice, probable position at noon is figured in ad- 
vance (dead reckoning) . The officer can then know at what 
time by the chronometer noon will occur. 

Very commonly, sights are worked up in detail before 
noon and an expression obtained which only requires the 
introduction of the observed altitude to obtain the latitude 
at once. 

Using D. R. longitude the G. M. time is known and the 
declination found. I. E. ; S. D. ; and dip are likewise known 
in advance. From D. R. latitude, working backwards an 
approximate altitude is found and R.. & P. for this altitude 
used to find an expression, composed of declination and cor- 
rections to altitude, which applied to observed altitude give 
latitude instantly. Performing this work in advance en- 
ables the officer to have his position immediately after noon. 
Knowing approximate altitude before taking the sight is 
also of great value on a cloudy day. 

Declination is found in the usual way. 

If declination and D. R. latitude are same name the dif- 
ference is Z. D., if different name the sum is Z. D. 

Subtract Z. D. from 90° to get an approximate altitude. 
The R. & P. for this altitude is used as correct. 



SIMPLE RULES AND PROBLEMIS IN NAVIGATION 129 

If declination and latitude are opposite names or if same 
names with declination greater apply correction to declina- 
tion and subtract from 90° to get the constant. 

If same names but latitude greater than declination apply 
correction with opposite sign to declination, i.e., add if — , 
subtract if +. The declination with correction is then added 
to 90° to get the constant. 

The observed altitude is in all cases subtracted from the 
constant. 

PROBLEM NO. 18 

July 5, 1919. Probable noon position: Lat. 41° 07' N. Long. 143° 
17' E. Index Error+ 1' 30". Dip 36 ft. 

Longitude in time 9h 33' 08". L. A. T., 5d Oh 00' 00" 

Prob.Lat. 41° 07' 00" N ^^^- ^^ ''' ''" 



Dec. 22° 54' 12" N g. A. T., 4d 14h 26' 52' 

Approx.Z.D. 18° 12' 48" N ^^'^'^' + ^' ''' 



Approx. Alt. 71° 47' 12" S q m. T. 14h 31' 00" or 

4d 14.5h 

R. & P. - 16" Dec. for 4d 14h 22° 54'.3 N 

Dip - 5' 53" Corr. for .5h - O'.l 



*■" 


16" 
5' 53" 


+ 


6' 09" 
15' 48" 


+ 
+ 


9' 39" 
1' 30" 



Dec. for 4d 14.5h 22° 54'.2 N 
S. D. 

LE. 

Total Alt. Corr. 11' 09" -f 

(Dec. and latitude same name, Dec. 22° 54' 12" N 

latitude greater). Subtract Corr. 11' 09" 



22° 43' 03' 
90° 00' 00' 



Const. 112° 43' 03" N 

Officer will prepare to take his sight when chronometer reads 2:31 
A. M. 

The Mer. Alt. of Sun's L. L. is now measured and found to be 71° 41' 
10", bearing S. It is subtracted from the expression worked out and gives 
latitude at once. 

Const. 112° 43' 03" N 

Obs. Alt. 71° 41' 10" S 



Lat. 41° 01' 53" N 



130 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 19 

Jan. 30, 1919. Probable noon position: Lat. 43° 17' N. Long. 61' 
11' W. Index Error -1' 20". Dip 36 ft. 

Longitude in time 41i 04' 44" L. A. T., 30d Oh 00' 00" 

Prob.Lat. 43M7'00"N ^^^^^ "^ ^^ ^^^ 



Dee. 17° 49' 06" S g. A. T. 4h 04' 44" 

Approx.Z.D. 61° 06' 06" N ^^- ^^^ -- _13^ 



Approx. Alt. 28 53 o4" b ^q^ 4 3Jj 

R. & P. - 1' 42" Dec.for30d4h 17° 49'.3 S 

Dip - 5' 53" Corr. for .3h 0'.2 

L E. - r 20" 



Dec.for30d4.3h 17° 49'.1 S 



8' 55" 
S. D. + 16' 18" 



Total Alt. Corr. + 7' 23" 

(Declination and latitude oppo- Dec. 17° 49' 06" S 

site names). Corr. + 7' 23" 



17° 56' 29' 
90° 00' 00' 



Const. 72° 03' 31" N 

Officer takes sight at 4:18 P. M. by chronometer and finds sun at its 
highest point has an altitude of 29° 00', bearing S. 

Const. 72° 03' 31" N 

Obs. Alt. 29° 00' 00" S 



Lat. 43° 03' 31" N 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 131 



PROBLEM NO. 20 

Aug. 8, 1919. Probable noon position: Lat. 31° 16' 10" S. Long. 
22° 10' E. Index Error+30". Dip 36 ft. 

Longitude in time Ih 28' 40". L. A. T., 8d Oh 00' 00" 

Prob.Lat. 3ri6'10"S ^""^^ '"^ ^^' ^" 

Dec. 16° 22' 54" N G.A.T,7d 23h 31' 20" 

Approx.Z.D. 47° 39' 04" S ^'»- ^^^ +__5^ 

Approx.Alt. 42° 20' 56" N ^- ^- %d Ifi'' ''" °' 



K. & P. - 57" Dee. for 7d 22h 16° 24'.0 N 

Dip - 5' 53" Corr. for 1.6h I'.l 






6' 


50" 


+ 


15' 


48" 




8' 


58" 


+ 




30" 



Dec. for 7d 23.6h 16° 22.'9 N 
S.D. 

LE. 

Total Alt. Corr. + 9' 28" 

(Declination and latitude oppo- Dec. 16° 22' 54" N 

site names). Gorr. -f 9' 28" 



16° 32' 22' 
90° 00' 00' 



Const. 73° 27' 38" S 

Sun will cross meridian when chronometer reads llh 36' 57" A. M. 
Altitude observed 42° 50', bearing N. 

Const. 73° 27' 38" S 

Alt. 42° 50' 00" N 



Lat. 30° 37' 38" S 



132 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 21 

Dec. 15, 1919. Probable noon position: Lat. 10° 12' S. Long. 60' 
00' W. Dip 36 ft. 



Longitude in tim 
Prob. Lat. 


.e41i 

10° 
23° 


12' 00" 
14' 36" 


S 

N 
S 


L. A. T., 15d 

Long. 

G. A. T. 

Eq. Time 

G. M. T. 

15d 

Dec.forl5d4h 
Corr. for. Ih 

Dec.forl5d3.9h 


Oh 00' 00" 
4h 00' 00" 


Dec. 


4h 00' 00" 


Approx. Z. D. 


13° 

76° 


02' 36" 

57' 24" 

12" 
5' 53" 


- 5' 05" 


Approx. Alt. 

R.&P. 
Dip 


3h 54' 55" or 
3.9h 

23° 14.'6 S 
O'.O 


S. D. 


+ 


6' 05" 
16' 18" 


23° 14'.6 S 


Total Alt. Corr. 


+ 


10' 13" 





(Declination and latitude same Dec. 23° 14' 36" S 

names, declination greater). Corr. -f 10' 13" 

23° 24' 49" 

90° 00' 00" 



Const. 66° 35' 11" N 

Officer takes sight at 3:55 P. M. by chronometer. Observed altitude 
76° 10', bearing S. 

Const. 66° 35' 11" N 

Obs. Alt. 76° 10' 00" S 



Lat. 9° 34' 49" S 



CHAPTER VIII 
LATITUDE BY MERIDIAN ALTITUDE OF STAR 

This example is worked the same as the previous one. 

The dechnation of a star having a very small annual 
cnange, it is only necessary to take out the minutes for the 
month, and the number of degrees on the side opposite the 
star used. 

Declination is found on page 95, Nautical Almanac. 

There is no Semi-diameter or Parallax for a star, so the 
meridian altitude is corrected as follows: 

Index Error as per sign if any. 

Dip (Table 14) subtract. 

Refraction (Table 20 A) subtract. 

Answer will be true altitude. 

Subtract true altitude from 90°. Answer will be Zenith 
Distance, to be named opposite name to star's bearing. 

Under Zenith Distance put down declination and apply 
as follows: 

Same names, add. 

Different names, subtract less from greater. 

Answer will be latitude. 

Name the latitude as follows: 

If added, will be named the same as the two of them. 

If subtracted, will be named the same as greater of two. 

FINDING TIME OF STARS' MERIDIAN PASSAGE 

From page 96 (Nautical Almanac) take out G. M. T. of 
transit of the star for the first day of the month. Then sub- 
tract from this time the correction given on page 97 (N. A.) 
for the day of the month to reduce the time to the date of the 
observation. This will be local mean time of transit, very 
closely. A further correction of 10^ for every 15° longitude 
added if E longitude, subtracted if W longitude, may be 
applied. 

133 



134 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

PROBLEM NO. 1 

Jan. 10, 1919. Find time of Meridian Passage of Star 
'' Spica.'^ 

Time of Transit Jan. 1 18h 38' 

Correction for lOd — 35' 



Time of Transit Jan. 10 18h 03' 

PROBLEM NO. 2 

Feb. 16, 1919. Find time of Meridian Passage of Star 
" A.rc turns '^ 

Time of Transit Feb. 1 17h 27' 

Correction for 16d — 59' 



Time of Transit Feb. 16 16h 28' 

PROBLEM NO. 3 

June 3, 1919. Find time of Meridian Passage of Star 
^' Canopus.'' 

Time of Transit June 1 Ih 46' 

Correction for 3d — 8' 



Time of Transit June 3 Ih 38' 

PROBLEM NO. 4 

May 12, 1919. Find time of Meridian Passage of Star 
" Sirius." 

Time of Transit May 1 4h 07' 

Correction for 12d - 43' 



Time of Transit May 12 3h 24' 

LATITUDE BY STAR 

PROBLEM NO. 1 

Nov. 12, 1919. Obs. Mer. Alt. *Rigel 26° 47' 10" S. Index Error 
-1'20". Dip 18 ft. 

Dec. 8° 17'.5 S 



Alt. 
LE. 


26° 47' 10" 
1' 20" 


True Alt. 

Z. D. 
Dec. 

Lat. 


90° 00' 00" 
26° 39' 46" 


Dip 


26° 45' 50" 
4' 09" 


63° 20' 14" N 
8° 17' 30" S 


Ref. 


26° 41' 41" 
1' 55" 


55° 02' 44" N 


True Alt. 


26° 39' 46" 





SIMPLE RZLES AND PROBLEMS IN NAVIGATION 135 

PROBLEM NO. 2 

Feb. 12, 1919. Obs. Mer. Alt. *Procyon 77° 18' 10" S. Index Error 
+20". Dip 16 ft. 

Dec. 5° 25'.8 N 



Alt. 
LE. 


77° 18' 10" 
4- 20" 


True Alt. 

Z. D. 
Dec. 

Lat. 


90° 00' 00" 

77° 14' 22" 


Corr. (46) 


77° 18' 30" 
4' 08" 


12° 45' 38" N 
5° 25' 48" N 


True Alt. 


77° 14' 22" 


18° 11' 26" N 



PROBLEM NO. 3 

Mar. 19, 1919. Obs. Mer. Alt. *Arcturus 36° 10' 20" N. Index 
Error +2' 40". Dip 20 ft. 

Dec. 19° 35'.9 N 



Alt. 
LE. 


36° 10' 20" 
+ 2' 30" 


True Alt. 

Z. D. 

Dec. 

Lat. 


90° 00' 00" 
36° 07' 17" 


Corr. (46) 


36° 13' 00" 
- 5' 43" 


53° 52' 43" S 
19° 35' 54" N 


True Alt. 


36° 07' 17" 


34° 16' 49" S 



PROBLEM NO. 4 

July 9, 1919. Obs. Mer. Alt. *Spica 49° 16' 25'' S. Dip. 18 ft. 
Dec. 10° 44'.6 S 



Obs. Alt. 
Corr. (46) 


49° 16' 25" 
4' 59" 


True Alt. 

Z. D. 
Dec. 

Lat. 


90° 00' 00" 
49° 11' 26" S 




49° 11' 26" 


40° 48' 34" N 
10° 44' 36" S 




30° 03' 58" N 



PROBLEM NO. 5 

Mar. 11, 1919. Obs. Mer. Alt. *Betelgeux 80° 10' 20" N. Dip 30 ft. 
Dec. 7° 23'.5 N 



Obs. Alt 
Corr. (46) 


80° 10' 20" 
- 5' 32" 


True Alt. 

Z. D. 
Dec. 

Lat. 


90° 00' 00" 

80° 04' 48" N 


True Alt. 


80° 04' 48" 


9° 55' 12" S 
7° 23' 30" N 




2° 31' 42" S 



136 SIMPIE RULES AND PROBLEMS IN NAVIGATION 

PROBLEM NO. 6 

Feb. 16, 1919. Obs. Mer. Alt. *Aldebaran 38° 15' S. Dip 28 ft. 
Dec. 16° 20'.8 N 



Obs. Alt. 
Corr. (46) 


38° 15' 00" 

6' 25" 


True Alt. 

Z. D. 
Dec. 

Lat. 


90° 00' 00" 

38° 08' 35" S 


True Alt. 


38° 08' 35" 


51° 51' 25" N 
16° 20' 48" N 




68° 12' 13" N 



PROBLEM NO. 7 

Nov. 21, 1919. Obs. Mer. Alt. *Sirius 41° 16' 00" S. Dip 40 ft. 
Dec. 16° 36'.4 S 



Obs. Alt. 
Corr. (46) 


41° 16' 00" 

7' 20" 


True Alt. 

Z. D. 
Dec. 

Lat. 


90° 00' 00" 
41° 08' 40" S 


True Alt. 


41° 08' 40" 


48° 51' 20" N 
16° 36' 24" S 




32° 14' 56" N 



PROBLEM NO. 8 

Apr. 6, 1919. Obs. Mer. Alt. *Fomalhaut 18° 17' 00" S. Dip 28 ft. 
Dec. 30° 03'.0 S 



Obs. Alt. 
Corr. (46) 


18° 17' 00" 
- 8' 06" 


True Alt. 

Z.D. 
Dec. 

Lat. 


90° 00' 00" 

18° 08' 54" S 


True Alt. 


18° 08' 54" 


71° 51' 06" N 
30° 03' 00" S 




41° 48' 06" N 



PROBLEM NO. 9 

May 12, 1919. Obs. Mer. Alt. *Antares 80° 16' 00" N. Dip 20 ft. 
Dec. 26° 15'.3 S 



Obs. Alt. 
Corr. (46) 


80° 16' 00" 
4' 33" 


True Alt. 

Z.D. 
Dec. 

Lat. 


90° 00' 00" 
80° 11' 27" N 


True Alt. 


80° 11' 27" 


9° 48' 33" S 
26° 15' 18" S 




36' 03' 51" S 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 137 

PROBLEM NO. 10 

July 16, 1919. Obs. Mer. Alt. *Fomalhaut 73° 36' 00" S. Index 
Error+1'40". Dip 24 ft. 

Dec. 30° 02'.6 S 



Obs. Alt. 
LE. 


73° 36' 00" 
+ 1' 40" 


True Alt. 

Z. D. 
Dec. 

Lat. 


90° 00' 00" 
73° 32' 35" S 


Corr. (46) 


73° 37' 40" 
5' 05" 


16° 27' 25" N 
30° 02' 36" S 




73° 32' 35" 


13° 35' 11" S 



PROBLEM NO. 11 

Apr. 6, 1919. Obs. Mer. Alt. *Regulus 50° 14' 20" S. Index Error 
4-1' 15". Dip 18 ft. 

Dec. 12° 21'.5 N 



Obs. Alt. 
LE. 


50° 14' 20" 
+ 1' 15" 


True Alt. 

Z. D. 
Dec. 

Lat. 


90° 00' 00" 
50° 10' 37" S 


Corr. (46) 


50° 15' 35" 

4' 58" 


39° 49' 23" N 
12° 21' 30" N 


True Alt. 


50° 10' 37" 


52° 10' 53" N 



PROBLEM NO. 12 

Dec. 26, 1919. Obs. Mer. Alt. *Sirius 36° 28' 30" S. Index Error 
-45". Dip 16 ft. 

Dec. 16° 36'.5 S 



Obs. Alt 
LE. 


36° 28' 30" 
45" 


True Alt. 

Z. D. 
Dec. 

Lat. 


90° 00' 00" 
36° 22' 31" S 


Corr. (46) 


36° 27' 45" 
- 5' 14" 


53° 37' 29" N 
16° 36' 30" S 




36° 22' 31" 


37° 00' 59" N 



CHAPTER IX 
LONGITUDE BY SUN 

The longitude of a place is the number of hours, minutes 
and seconds east or west of the meridian of Greenwich, 
which is Long. 0°, expressed in degrees, minutes and seconds. 

A chronometer is an ordinary clock of the finest make, 
with a 12-hour face, and keeps the time of Greenwich. 

The astronomical day is explained under Definitions, and 
begins at noon and ends at noon. 

In all instances in this example if chronometer time is 
A. M. add 12 to the hours and date one day back. 

P. M. chronometer time keeps same date as example. 

Put down chronometer time and correct fast or slow as 
given. Answer will be Greenwich Mean Time expressed 
G. M. T. 

Take out Sun's declination for Greenwich mean time. 

The polar distance is the angular distance of a heavenly 
body from the pole nearest the observer. To find polar dis- 
tance follow rule : 

If latitude and declination are different names, add 90° 
to dechnation. 

If latitude and declination are same names, subtract 
dechnation from 90°. 

A chronometer always keeps the time of a day of exactly 
24 hours, which is called a Mean day, but the sun's time 
which is known as Apparent Time, changes a Httle every 
day. The difference between mean time and apparent time 
is called the equation of time. 

Take from the almanac equation of time for Greenwich 
date and time, and apply it to G. M. T. as by sign given in 
almanac. 

Answer will be Greenwich Apparent Time expressed 
G. A. T. 

13S 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 139 

Correct observed altitude of sun as follows: 

Index error as per sign, if any. 

Semi-Diameter from almanac. Add for Lower Limb. 
Subtract for Upper. 

Dip (Table 14) subtract. 

Refraction and parallax (Table 20B) subtract. 

Answer will be true altitude. 

Add together true altitude, latitude and polar distance, 
and divide sum by 2. Answer will be half sum. 

Subtract true altitude from half sum. Answer will be 
remainder. 

From Table 44 (Bowditch) take out the following loga- 
rithms to the nearest second of arc: 

Secant of latitude. Rejecting 10 from index number. 

Cosecant of polar distance. Rejecting 10 from index 
number. (See note.) 

Cosine of half sum. 

Sine of remainder. 

Add these four logarithms together, and subtract 10 
from index number. 

Note. — If polar distance exceeds 90° take Secant of 
declination instead. 

Logarithm Haversine (Table 45) that agrees with sum of 
logarithms will be the Local Apparent Time, expressed 
L. A. T. 

If sight was taken in A. M. read hours and minutes 
from bottom, and seconds in right-hand column, and date 
one day back. 

If sight was taken in P. M. read hours and minutes from 
top, and seconds in left-hand column, and date same as 
example. 

Under L. A. T. put down G. A. T. If both are same date 
subtract less from greater, if different dates add 24 hours to 
greatest date, and then subtract less from greater. Answer 
will be longitude in time. 

Multiply hours of longitude in time by 60, and add the 
minutes. Divide the minutes by 4, and the result will be 
degrees of longitude. If any minutes are left multiply by 
60 and add the seconds, divide by 4, and the result will be 
minutes of longitude. If any seconds are left multiply 
by 60 and divide by 4, and the result will be seconds of longi- 
tude. 

If the Greenwich time is best, the longitude is west. 

If the Greenwich time is least, the longitude is east. 



140 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



FINDING GREENWICH DATE AND TIME 

The Greenwich time and date is absolutely necessary 
to be found correctly in this example. 

In some of the problems given in this book the reading of 
the chronometer is given A. M. or P. M., others longitude 
by dead reckoning is given; in others the Greenwich date and 
time is given. 

Below will be found the different methods that an exam- 
ple may be given, and the explanation of how the Greenwich 
date may be found. 

If the chronometer reads A. M. and no longitude by 
D. R. is given, add 12 hours to the time, and date one day 
back. 

For example: Jan. 25th P. M. at ship. Chronometer read 
lOh 16' 28'' A. M. 

Greenwich date and time will be Jan. 24th 22h 16' 28". 

If chronometer reads P. M. and no longitude by D. R. is 
given, the Greenwich date and time will be the same as the 
example. 

For example: Jan. 25th A. M. at ship. Chronometer 
read Ih 16' 28" P. M. 

Greenwich date and time will be Jan. 25th Ih 16' 28". 

If the Greenwich date is given, the chronometer is put 
down in the following manner: 

Jan. 25th A. M. at ship. Chronometer read Jan. 24th 
llh 16' 28". 

Greenwich date and time will be Jan. 24th llh 16' 28". 

If the approximate ship's time and longitude by D. R. 
are given in an example, and the chronometer reading with- 
out stating whether it is A. M. or P. M. the student must be 
able to determine whether the chronometer is A. M. or P. M. 
in order to convert it into astronomical time. 

For example, if problem was given in following manner: 

Jan. 26th about 7 A. M. at ship. Longitude by D. R. 
90° W. Chronometer read Ih 10". 

Now as the difference between ship's time and Green- 
wich time is the longitude in time, we have for the above 
example a longitude in time of 6 hours. 

In west longitude the Greenwich time is the largest. So 
if it is about 7 A. M. at ship, it must be Ih 10' P. M. at Green- 
which. Or, Greenwich date Jan. 26th Ih 10'. 

Now presuming this example was in longitude by D. P- 
90° E. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 141 

In east longitude the ship's time is the largest. So if it 
is about 7 A. M. at ship, it must be Ih 10' A. M. at Green- 
wich. Or, Greenwich date Jan. 25th 13h 10'. 

This will explain practically all the methods of finding 
Greenwich date, and if the student will read his problem 
carefully he should have no trouble. 

It must always be remembered that the astronomical 
day begins at noon of the civil day, and ends at noon, and 
a 24-hoiir face clock must be imagined. 

PROBLEM NO. 1 

Jan. 31, 1919, A. M. Obs. Alt. Sun's L. L. 13° 54' 00". Dip 36 ft. 
Chronometer read 2h 46' 17" P. M., fast 34' 34". Lat. 25° 44' N. 



Chron. 
Fast 

G. M. T., 31d 
Eq. Time 

G. A. T., 31d 



Altitude 
S. D. 



Dip 



R. & P. 

True Alt. (h) 

Lat. 

P.D. 



Half Sum (s] 
h 



2h 46' 17" 
34' 34" 

2h 11' 43" 
13' 30" 

Ih 58' 13" 



13° 

+ 


54' 
16' 


00" 
15" 


14° 


10' 
5' 


15" 
53" 


14° 


04' 
3' 


22" 
40" 


14° 

25° 

107° 


00' 
44' 
34' 


42" 
00" 
06" 


2)147' 


' 18 


' 48" 


73° 
14° 


39' 
00' 


24" 
42" 



59° 38' 42' 



L. A. T., 30d 
G. A. T., 31d 

Long. 



Dec, 31d, 2h 
Corr. .2h 

Dec. 31d 2.2h 



Dec. 
P.D. 



Sec. 
Csc 



Cos 



Sin 

Log. Hav. 



17° 


34'.2 S 
O'.l 


17° 

90° 
17° 


34'.1 S 

00' 00" 
34' 06" 



107° 34' 06' 



.04536 
.02074 



9.44931 

9.93596 
9.45137 



93° 48' W 



19h 43' 01" 

Ih 58' 13" 

6h 15' 12" or 



142 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 2 

Jan. 30, 1919, P. M. Obs. Alt. Sun's L. L. 18° 32'. Dip 36 ft. 
Chron. read lOh 42' 46" P. M., fast 34' 28". Lat. 27° 12' N. 



Chron. 
Fast 

G. M. T., 30d 

Eq. Time 

G. A. T. 



lOh 42' 46" 
34' 28" 

lOh 08' 18" 
13' 23" 

9h 54' 55" 



Dec. 30d lOh 
Corr. .Ih 

Dec. 30d lO.lh 
P.D. 



17° 45'.2 S 
O'.l 

17° 45'. 1 S 
90° 00' 00" 

107° 45'.1 



Altitude 
S. D. 



Dip 



R. &P. 

True Alt 

Lat. 

P.D. 



s-h 



18° 32' 00" 
+ 16' 15" 



18° 


48' 
5' 


15" 

53" 


18° 


42' 

2' 


22" 
43" 


18° 

27° 

107° 


39' 
12' 
45' 


39" 
00" 
06" 


5)153° 


36' 


45" 


76° 

18° 


48' 
39' 


22" 
39" 



58° 08' 43' 



Sec 
Csc 



Cos 



Sin 

Log. Hav. 



.05089 
.02118 



9.35841 



9.92911 
9.35959 



L A. T, 30d 
G. A. T., 30d 

Long. 



91° 34' W 



3h 48' 39" 
9h 54' 55" 

6h 06' 16" or 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 143 



PROBLEM NO. 3 

Mar. 11, 1919, A. M. Obs. Alt. Sun's L. L. 28° 13' 00". Dip 38 ft. 
Chronometer read 3h 12' 15" A. M. Lat. 31° 46' S. 

G. M. T., lOd 15h 12' 15" Dec. lOd 14h 4° 10'.6 S 

Eq. Time - 10' 28" Corr. for 1.2h - 1'.2 S 



G. A. T., lOd 15h 01' 47" Dee. lOd 15.2h 4° 09'.4 S 

90° 00' 



P. D. 85° 50'.6 



Alt. 28° 13' 00" 

S. D. + 16' 06" 



Dip 



28° 


29' 
6' 


06" 
02" 


28° 


23' 
1' 


04" 
40" 


28° 
31° 

85° 


21' 
46' 
50' 


24" 
00" 
36" 


2)145° 


58' 


00" 



R. &P. 

True Alt. 

Lat. 31° 46' 00" Sec .07048 

P. D. 85° 50' 36" Csc .00114 



72° 59' 00" Cos 9.46635 

44° 37' 36" Sin 9.84664 



Log. Hav. 9.38461 



L. A. T., lOd 20h 04' 01" 

G. A. T., lOd 15h 01' 47" 



Long. 5h 02' 14" or 

75° 33' 30" E 



144 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 4 

Jan. 31, 1919, P. M. Obs. Alt. Sun's L. L. 18° 32'. Dip 36 ft. 

Chronometer read lOh 42' 46" A. M., fast 34' 28". Lat. 27° 12' N. 



Chron. 
Fast 


22h 42' 46" 
- 34' 28" 


Dec. 30d 22h 
Corr. for .Ih 

Dec. 30d 22. Ih 
P.D. 


17° 37'.0 S 
O'.l 


G. M. T., 30d 

Eq. Time 


22h 08' 18" 
13' 28" 


17° 36'.9 
90° OO'.O 


G. A. T., 30d 

Alt. 
S.D. 


21h 54' 50" 

18° 32' 00" 
+ 16' 18" 


107° 36'.9 



18° 


48' 18" 
5' 53" 


18° 


42' 25" 

2' 43" 


18° 

27° 

107° 


39' 42" 
12' 00" 
36' 54" 


2)153° 


28' 36" 



Dip 



R.&P. 

h 

Lat. 27° 12' 00" Sec .05089 

P.D. 107° 36' 54" Csc .02086 



s 76° 44' 18" Cos 9.36059 

s-h 58° 04' 36" Sin 9.92879 



Log. Hav. 9.36113 



L. A. T., 31d 3h 49' 06' 

G A. T, 30d 21h 54' 50' 



Long. 5h 54' 16" or 

88° 34' E 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 145 



PROBLEM NO. 5 

Mar. 10, 1919, A. M. OLs. Alt. Sun's L. L. 21° 00' 00". Dip 38 ft 

Chronometer read Ih 07' 56" P. M. Lat. 31° 19' N. 



Dip 



R. &P. 

h 

Lat. 
P. D. 



s 



21° 


16' 06" 
6' 02" 


21° 


10' 04" 
2' 21" 


21° 

31° 

94° 


07' 43" 
19' 00" 
23' 18" 


2)146° 


50' 01" 



73° 25' 00' 
52° 17' 17' 



Sec 
Csc 



Cos 
Sin 



G. M. T., lOd 
Eq. Time 


Ih 07' 56" 
- 10' 37" 


Dec. lOd Oh 
Corr. l.Oh 

Dec. 10 d. Ih 
P. D. 


4° 24'.3 S 
I'.O 


G.A.T. lOd 


Oh 57' 19" 

21° 00' 00" 
+ 16' 06" 


4° 23'.3 S 
90° OO'.O 


Alt. 
S.D. 


94° 23'.3 



Log. Hav. 



.06839 
.00127 



9.45547 
9.89823 

9.42336 



L. A. T„ 9d 
G. A. T., lOd 

Long. 



76° 18' 15" W 



19h 52' 06" 
Oh 57' 19" 

5h 05' 13" W or 



146 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 6 

July 5, 1919, A. M. Obs. Alt. Sun's L. L. 18° 15'. Dip 38 ft. Chro- 
nometer read lOh 15' 25" A. M., slow 12' 10". Lat. 37° 15' N. 



18° 


30' 
6' 


45" 
02" 


18° 


24' 
2' 


43" 
45" 


18° 
37° 
67° 


21' 
15' 
07' 


58" 
00" 
30" 


2)122° 


44' 


28" 



Chron. 
Slow 


22h 15' 25" 
+ 12' 10" 


Dec. 4d 22h 
Corr. .4h 

Dec. 
P. D. 


22° 52'.6 N 
O'.l 


G. M. T. 

Eq. Time 


22h 27' 35" 
- 4' 11" 


22° 52'.5 
90° OO'.O 


G. A. T, 4d 

Alt. 
S.D. 


22h 23' 24" 

18° 15' 00" 
H- 15' 45" 


67° 07'.5 



Dip 



R.&P. 

h 

Lat. 37° 15' 00" Sec .09909 

P. D. 67° 07' 30" Csc .03557 



s 61° 22' 14" Cos 9.68047 

s-h 43° 00' 16" Sin 9.83382 



Log. Hav. 9.64895 



L. A. T., 4d 18h 24' 59' 

G. A. T., 4d 22h 23' 24' 



Long. 3h 58' 25" or 

59° 36' 15" W 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 147 



PROBLEM NO. 7 

July 5, 1919, A. M. Obs. Alt. Sun's L. L. 14° 28' 30". Dip 21 ft. 
Chronometer read 4h 16' 28" A. M., slow 14' 28". Lat. 26° 33' N. 

Chron 
Slow 

G. M. T. 
Eq. Time 

G. A. T. 4d 

Alt. 
S. D. 



Dip 



R.&P. 

h 

Lat. 
P. D. 



s-h 



16h 16' 28" 
+ 14' 28" 


Dec. 4d 
Corr. .51 

Dec. 4d 
P. D. 

Sec 
Csc 

Cos 
Sin 

Log. 
15" E 


161i 
16.5h 

Hav. 

18h 21' 
16h 26' 


22° 


53'.9 N 
O'.l 


16h 30' 56" 
4' 09" 


22° 
90° 


53'.8 
00' 


161i 26' 47" 

14° 28' 30" 
4- 15' 45" 


67° 

48" 

47" 


06'.2 


14° 44' 15" 
4' 29" 




14° 39' 46" 
- 3' 30" 




14° 36' 16" 
26° 33' 00" 
67° 06' 12" 

2)108° 15' 28" 

54° 07' 44" 
39° 31' 28" 


.04840 
.03564 

9.76787 
9.80373 


L. A. T., 4d 
G. A. T., 4d 


9.65564 


Long. 

28° 45' 


Ih 55' 


01" E 


or 



148 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 8 

Jan. 31, 1919, P. M. Obs. Alt. Sun's L. L. 23° 16'. Dip 36 ft. 
Chronometer read lOh 38' 38" P. M., fast 34' 37". Lat. 24° 55' N. 

Chron. lOh 38' 38" Dec. 31d lOh 17° 28'.7 S 

Fast. - 34' 37" Corr. .Ih - O'.l 



G. M. T. 31d lOh 04' 01" Dec. 31d lO.lh 17° 28'.6 S 

Eq. Time - 13' 33" 90° OO'.O 



G. A. T. 9h 50' 28" P. D. 107° 28'.6 

Alt. 23° 16' 00" 

S. D. + 16' 16" 



23° 32' 16' 
Dip - 5' 53' 



23° 26' 23" 
R. & P. - 2' 05" 



h 

Lat. 
P. D. 


23° 24' 18" 

24° 55' 00" 

107° 28' 36" 


45 


Sec 
Csc 

Cos 

Sin 

Log. 
" W 


Hav. 

3h 30' 
9h 50' 


57" 

28" 


W 


.04243 
.02052 


s 
s-h 


2)155° 47' 54" 

77° 53' 57" 
54° 29' 39'^^ 

L. A. T., 31d 
G. A. T. 31d 

Long. 

94° 52' 


9.32146 
9.91066 




9.29507 




6h 19' 


31" 


or 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 149 



PROBLEM NO. 9 

Dec. 15, 1919, A. M. Obs. Alt. Sun's L. L. 28° 16' 15". Dip 40 ft. 
Chronometer read 4h 16' 28" P. M., slow 14' 28". Lat. 26° 33' S. 



Chron. 
Slow 


15d 


4h 16' 28" 
+ 14' 28" 


Dec. 15d 4h 
Corr. for .5h 

Dec. 15d 4.5h 
P. D. 


23° 14'.6 S 
+ O'.l 


G. M. T. 
Eq. Time 


4h 30' 56" 
+ 5' 04" 


23° 14'.7 S 
90° 00' 


G. A. T. 

Alt. 
S. D. 


4h 36' 00" 

28° 16' 15" 
+ 16' 18" 


66° 45'.3 



28° 


32' 


33" 


— 


6' 


12" 


28° 


26' 


21" 


— 


1' 


39" 


28° 


24' 


42" 


26° 


33' 


00" 


66° 


45' 


18" 


2)121° 


43' 


00" 



Dip 



R. &P. 

h 

Lat. 26° 33' 00" Sec .04840 

P. D. 66° 45' 18" Csc .03676 



s 60° 51' 30" Cos 9.68750 

s-h 32° 26' 48" Sin 9.72958 



Log. Hav. 9.50224 



L. A. T., 14d 19h 25' 27" 

G. A. T., 15d 4h 36' 00" 



Long. 9h 10' 33" W or 

137° 38' 15" W 



150 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 10 

Oct. 24, 1919, A. M. Obs. Alt. Sun's L. L. 18° 26' 15". Dip 40 ft. 
Chronometer read 2h 08' 03" A. M., fast 58' 13". Lat. 3° 21' S. 



Chron. 
Fast 


23d 
23d 


L. 
G. 

Lo 


14h 08' 03" 
58' 13" 


Dec. 23d 12h 
Corr. for 1.2h 

Dec. 23d 13.2h 
P.D. 

Sec 
Csc 

Cos 

Sin 

Log. Hav. 

19h 13' 
13h 25' 


11° 

+ 


18'.6 S 
I'.l 


G. M. T. 

Eq. Timt 


13h 09' 50" 
+ 15' 33" 


11° 
90° 


19'.7 S 
00' 


G. A. T. 

Alt. 
S. D. 


13h 25' 23" 

18° 26' 15" 
+ 16' 06" 


78° 

04" 
23" 


40'.3 


Dip 


18° 42' 21" 
6' 12" 




R. &P. 


18° 36' 09" 
2' 43" 




h 

Lat. 

P.D. 


18° 33' 26" 
3° 21' 00" 

78° 40' 18" 


.00074 
.00855 


s 
s-h 


2)100° 34' 44" 

50° 17' 22" 
31° 43' 56" 

A. T., 23d 
A. T., 23d 

•ng. 

86° 55' 


9.80544 
9.72094 




9.53567 




5h 47' 
15" E 


41" E 


or 



CHAPTER X 
NOON POSITION SIGHTS 

The following problems are worked the same as the fore- 
going longitude sights as far as obtaining the longitude at 
sight. 

In working a sight for longitude the correct latitude of 
the place at time of sight must be used. 

In this problem the latitude at noon is given, and the lat- 
itude at sight must be found by taking from Table 2 (Bow- 
ditch) the difference of latitude and departure for the 
course and distance sailed between sight and noon. 

If the sight is taken in A. M. the name of the latitude 
difference north or south must be reversed to work the 
latitude back to sight. 

If taken in P. M. the name of the latitude difference 
stays the same. 

By applying the difference of latitude to latitude at noon, 
will be found the latitude at sight, which is the latitude to 
be used in working the problem. 

The middle latitude is then found by adding together 
latitude at noon and latitude at sight, and dividing sum 
by 2. 

Enter Table 2 with middle latitude as a course and look 
for departure in latitude column. In the distance column 
opposite will be difference of longitude in miles. 

If sight is taken in P. M. the name of the difference of 
longitude east or west must be reversed to work the prob- 
lem back to noon. 

If sight is A. M. the name of the difference of longitude 
stays the same. 

The chronometer is corrected for the original error slow 
or fast, and the number of days and tenths of a day from 
date of original error to Greenwich date are figured out, 
and multiplied by daily rate ; this will give the accumulated 
rate. 

This accumulated rate is then applied to chronometer, 
and the result will be G. M. T. 

The example is then worked as in previous problem, and 
the longitude at sight is obtained. 

By applying the difference of longitude to the longitude 
at sight, will give the longitude at noon. 

This will give ship's noon position. 

151 



152 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

PROBLEM NO. 1 

Feb. 10, 1919, A. M. Obs. Alt. Sun's L. L. 9° 09' 50". Index Error 
-3' 20". Dip 18 ft. Chronometer read Feb 9, 9h 59' 25" which was 
fast on Jan. 10, 34' 12" and losing 10".8, daily. Lat. at noon 50° 16' 
24" N. Ship's run from sight to noon S 56° W (true) 38 miles. 



Chron. 
Fast 


9h 59' 25" 
34' 12" 


30.4 days 
10".8 


Ace. Rate 


9h 25' 13" 

- 5' 28" 


' ■ 328" . 
Dec. 9d 8h 
Corr. L5h 

Dec. 9d 9.5h 

P. D. 

Lat. Noon 
Diff. Lat. 

Lat. at Sight 

At. md. Lat 
miles; DiiT. l.ong 


Ace. rate or 5' 28" 

14° 48'.5 
i'.2 


G. M. T. 9d 

Eq. Time 


9h 30' 41" 

- 14' 22" 


14° 47'.3 S 
90° 00' 


G. A. T. 9d 


9h 16' 19" 

9° 09' 50" 
3' 20" 


104° 47'.3 

50° 16' 24" N 
21' 12" 


Alt. 
LE. 


50° 37' 36" N 

50°; Dep. 31.5 
49' W 



9° 
+ 


06' 
16' 


30" 
12" 


9° 


22' 

4' 


42" 
09" 


9° 


18' 
5' 


33" 
33" 


9° 

50° 

104° 


13' 
37' 

47' 


00" 

36" 

18" 


2)164° 


37' 


54" 



S.D. 
Dip 

R. & P. 

True Alt. 

Lat. 50° 37' 36" Sec .19765 

P. D. 104° 47' 18" Csc .01463 

2) 164° 37' 54" 

s 82° 18' 57" Cos 9.12617 

s-h 73° 05' 57" fSin 9.98083 



Log. Hav. 9.31928 

L. A. T. 9d 20h 22' 36" 

G. A. T. 9d 9h 16' 19" 



Long. Sight llh 06' 17" or 

166° 34' 15" E 
Diff. Long. 49' 00" W 



Long. Noon 165° 45' 15" E 



3IMPLE RULES AND PROBLEMS IN NAVIGATION 153 

PROBLEM NO. 2 

Jan. 31, 1919, A.M. Obs. Alt. Sun's L.L.15°08'. Dip 30 ft. Chronom- 
eter read 2h 45' 49" P. M. which was fast on Jan. 11th, 31' 34" and gaining 
9" daily. Lat. at noon 25° 31' 17" N. Ship's run from sight to noon 
S 26° W (true) 57 miles. 



Chron. 
Fast 


2h 45' 49" 
- 31' 34" 


20.1 days 
9" 


Ace. Rate 


2h 14' 15" 
3' 01" 


180".9 I 

Lat. Noon 
Diff. Lat. 

Lat. Sight 

At Mid. Lat. 26°: 
Diff. Long. 28' W. 

Dec. 31d 2h 
Corr. .2h 

Dec. 31d 2.2h 
P.D. 


Lcc. Rate 

25° 31' 17" N 
51' 12" N 


G. M. T. 31d 

Eq. Time 


2h 11' 14" 
13' 30" 


26° 22' 29" N 
; Dep. 25.0 miles, 

17° 34'.2 S 
.1' S 


G. A. T. 31d 


Ih 57' 44" 

IS*' 08' 00" 
4- 16' 15" 




17° 34M S 
90° 00' 


Obs. Alt. 
S.D. 


107° 34'.1 



15° 24' 15" 
Dip - 5' 53" 



15° 18' 22' 
R. & P. - 3' 22' 



h 

Lat. 

RD. 


15° 15' 

26° 22' 

107° 34' 


00" 

29" 
06" 


Sec 
Csc 

Cos 
Sin 

Log. 


Hav. 

19h 50' 
lh57' 


50" 
44" 


W( 

W 

W 

W 


.04774 
.02074 




2)149° 11' 


35" 




6 

s-h 


74° 35' 
59° 20' 

L. A. T. 30d 
G. A. T. 31d 

Long, at Sight 

Diff. Long. 

Long, at Noon 


48" 
48" 


9.42425 
9.93463 




9.42736 




6h06' 
91° 43' 

28' 


54" 
30" 
00" 


Dr 




92° 11' 


30" 





154 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 3 

Jan. 2, 1919, A. M. Obs. Alt. Sun's L. L. 49° 10'. Index Error 
-2' 40". Dip 14 ft. Chronometer read 7h 08' 50" A. M., which was 
slow on Dec. 7, 19' 10".6 and losing 9".8 daily. Lat. at noon 37° 21' 
36" S. Ship's run from sight to noon S 45° W (true) 32 miles. 



Chron. 
Slow 


19h 08' 50" 
4- 19' 10" 


25.8 
9".8 

253" 

Dec. Id 18h 
Corr. 1.5h 

Dec. Id 19.5h 

P. D. 

Lat. at Noon 
Diff. Lat. 

Lat. at Sight 

Sec 
Csc 

Cos 
Sin 

Log. Hav. 

21h 01' 
19h 28' 


days 


Ace. Rate 


19h 28' 00" 
+ 4' 13" 


Ace. Rate 

23° 00'.6 S 
0'.3 


G. M. T. Id 
Eq. Time 


19h 32' 13" 
3' 42" 


23° 00'.3 
90° OO'.O 


G. A. T. Id 


19h 28' 31" 

49° 10' 00" 
- 2' 40" 




66° 59'.7 

37° 21' 36" S 
22' 36" N 


Obs. Alt. 
LE. 


36° 59' 00" S 


S.D. 


49° 

4- 


07' 20" 
16' 18" 




Dip 


49° 


23' 38" 
3' 40" 




R. &P. 


49° 


19' 58" 
45" 




h 

Lat. 
P. D. 


49° 
36° 
66° 


19' 13" 
59' 00" 
59' 42" 


.09756 
.03599 


s 
s-h 


2)153° 17' 55" 

76° 38' 58" 
27° 19' 45" 

L. A. T. Id 
G. A. T. Id 

Long, at Sight 

Diff. Long. 

Long, at Noon 


9.36344 
9.66191 




9.15890 

28" 
31" 




lh32' 
23° 14' 

28' 


57" or 

15" E 

W 




22° 46' 


15" E 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 155 

PROBLEM NO. 4 

Oct. 17, 1919, P. M. Obs. Alt. Sun's L. L. 16° 19' 15". Dip 28 ft. 
Chronometer read llh 55' 03" P. M., which was fast on Sept. 23, 8' 23" 
and gaining 8. "2 daily. Latitude at noon 22° 35' 48" S. Ship's run from 
noon to sight N 18° W (true) 42 miles. 



Alt. 
S. D. 



Dip. 



R.&P. 

h 

Lat. 

P.D. 



s-h 



Chron. 

Fast 


llh 55' 03" 

- 8' 23" 


24.5 

8".2 

201" 

Dec. 17d lOh 
CoiT. 1.7h 

Dec. 17d ll.'7h 

P.D. 

Lat. Noon 
Diff. Lat. 


days 


Ace. Rate 


llh 46' 40" 
- 3' 21" 


Ace. Rate 

9° 07'.3 S 
+ 1'.5 


G. M. T. 17d 
Eq. Time 


llh 43' 19" 
+ 14' 31" 


9° 08'.8 
90° 00' 


G. A. T. 17d 


llh 57' 50" 




80° 51'.2 

22° 35' 48" 
39' 54" 



s 

N 



Lat. Sight 21° 55' 54" S 

At Mid. Lat. 22°; Dep. 13.0miles; 
Diff. Long. 14' E. 



16° 19' 15" 

H- 16' 06" 


Sec 
Csc 

Cos 
Sin 

Log. Hav. 

5h 03' 
llh 57' 

6h 54' 

103° 36' 

14' 


24" 
50" 

26" 
30" 


or 
W 
E 

W 




16° 35' 21" 
5' 11" 




16° 30' 10" 
- 3' 06" 




16° 27' 04" 
21° 55' 54" 
80° 51' 12" 

2)119° 14' 10" 

59° 37' 05" 
43° 10' 01" 


.03262 
.00556 

9.70394 
9.83513 


L.A.T. 17d 
G.A.T.19d 

Long, at Sight 

Diff. Long. 


9.57725 


Long, at Noon 


103° 


22' 


30" 





156 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

PROBLEM NO. 5 

Dec. 1, 1919, A. M. Obs. Alt. Sun's L. L. 15° 18' 12". Dip 26 ft. 
Chronometer read Nov. 30th, 9h 02' 05", which was slow on Nov. 10th 
3' 55", and gains 7".8 daily. Latitude at noon 18° 16' N. Ship's run 
from sight to noon N 28° E (true) 58 miles. 



Chron. 
Slow 


9h 02' 05" 
+ 3' 55" 


Lat. 
Diff. 

Lat. 


20.4 

7".8 

159" 

at Noon 
, Lat. 

at Sight 


days 

Ace. Rate 

18° 16' 
51' 




Ace. Rate 


9h 06' 00" 
- 2' 39" 


00" N 

12" S 


G.M.T.30d 
Eq. Time 


9h 03' 21" 
-f 11' 24" 


17° 24' 


48" N 


G.A.T.30d 


9h 14' 45" 



At Mid. Lat. 18°; Dep. 27.2 
miles; Diff. Long. 28'.5 E. 





15° 18' 
-}- 16' 


12" 
15" 


Dec. 3( 
Corr. 1.: 

Dec. 30 
P.D. 

Sec 
Csc 

Cos 

Sin 

Log. 


)d 8h 
2h 

d9.2h 

Hav. 

19h 40' 
9h 14' 


21° 34'.9 S 
+ 0'.5 




21° 35'.4 S 
90° 00' 


Obs. Alt. 
S. D. 


111° 35'.4 


Dip 


15° 34' 
5' 


27" 
00" 




R. &P. 


15° 29' 
3' 


27" 
19" 




Trueh 

Lat. 

P.D. 


15° 26' 

17° 24' 

111° 35' 


08" 
48" 
24" 


.02037 
.03159 


s 


2)144° 26' 

72° 13' 
56° 47' 

L. A. T. 30d 
G. A. T. 30d 

Long, at Sight 

Diff. Long. 

Long, at Noon 


20" 

10" 
02" 


9.48483 
9.92252 




9.45931 

23" 

45" 




lOh 25' 
156° 24' 

28' 


38" or 
30" E 
30" E 




156° 53' 


00" E 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 157 

PROBLEM NO. 6 

May 3, 1919, A. M. Obs. Alt. Sun's L. L. 28° 49'. Dip 30 ft. Chro- 
nometer read 8h 03' 02" A. M., which was slow on Apr. 7, 3' 28", an^ 
gaining 2". 8 daily. Latitude at noon 28° 16' 28" N. Ship's run from 
sight to noon S 69° W (true) 73 miles. 



Chron. 
Slow 


20h 03' 02" 

+ 03' 28" 


25.8 di 
2".8 

72" Ac 

Dec. 2d 20h 
Corr. .Ih 

Dec. 2d 20.1h 

P. D. 

Lat. at Noon 
Diff. Lat. 

Lat. at Sight 

At Mid. Lat. 
miles; Diff. Long. 


lys 


Ace. Rate 


20h 06' 30" 
1' 12" 


!c. Rate 

15° 23'.5 N 
O'.l 


G. M. T. 2d 
Eq. Time 


20h 05' 18" 
+ 03' 06" 


15° 23'.6 N 
90° OO'.O 


G. A. T. 2d 


20h 08' 24" 

28'' 49' 00" 
+ 15' 54" 




74° 36'.4 

28° 16' 28" N 
26' 12" N 


Obs. Alt. 
S.D. 


28° 42' 40" N 

29°; Dep. 68.2 
77' W. 



29° 04' 54' 
Dip - 5' 22' 



28° 59' 32" 
R. & P. - 1' 37" 



True Alt. 
Lat. 
P. D. 


28° 57' 
28° 42' 
74° 36' 

2)132° 16' 


55" 
40" 
24" 

59" 


Sec 
Csc 








.05698 
.01589 


B 

s-h 


66° 08' 
37° 10' 


30" 
35" 


Cos 

Sin 

Log. Hav. 






9.60690 
9.78123 




9.46100 




L. A. T. 2d 
G. A. T. 2d 

Long, at Sight 

Diff. Long. 

Long, at Noon 






19h 39' 
20h 08' 


49" 

24" 


or 
W 
W 

W 






28' 
7° 08' 
1° 17' 


35" 

45" 
00" 






8" 25' 


45" 





158 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 7 

Apr. 23, 1919, A. M. Obs. Alt. Sun's L. L. 23° 15'. Dip 26 ft. 
Chronometer read Oh 03' 12" A. M., which was slow on Mar. 16th, 4' 
28", and gaining 11".7 daily. Latitude at noon 27° 23' S. Ship's run 
from sight to noon N 28° E (true) 62 miles. 



Chron. 
Slow 


12h 03' 12" 
+ 04' 28" 


37.5 days 
11".7 


Ace. Rate 


12h 07' 40" 
- 07' 19" 


439" Ace. Rate 

Dec. 22d 12h 12° 06' N 
90° 00' 


G.M.T.22d 
Eq. Time 


12h 00' 21" 
+ 01' 28" 


P. D. 102° 06' 

Lat. at Noon 27° 23' 00" S 
Diff. Lat. 54' 42" S 


G.A.T.22d 


12h 01' 49" 

23° 15' 00" 
4- 15' 54" 


Obs. Alt. 
S.D. 


Lat. at Sight 28° 17' 42" S 

At Mid. Lat. 28°; Dep. 29.1 
miles; Diff. Long. 33' E. 


Dip 


23° 30' 
5' 


54" 
00" 




R.&P. 


23° 25' 

2' 


54" 
05" 




True Alt. (h] 

Lat. 

P. D. 


1 23° 23' 

28° 17' 
102° 06' 


49" 
42" 
00" 


Sec .05526 
Csc .00976 


8 

s-h 


2)153° 47' 
76° 53' 
53° 29' 

L. A. T. 22d 
G. A. T. 22d 

Long, at Sight 

Diff. Long. 

Long, at Noon 


31" 
46" 

57" 


Cos 9.35550 
Sm 9.90518 




Log. Hav. 9.32570 

20h 20' 51" 
12h 01' 49" 




8h 19' 02" or 

124° 45' 30" E 

33' E 




125° 18' 30" E 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 159 



PROBLEM NO. 8 

Nov. 28, 1919, A. M. Obs. Alt. Sun's L. L. 50° 25'. Dip 30 ft. 
Chronometer read 9h 33' 10" A. M., which was fast on Oct. 22d, 3' 28" 
and losing 4."7 daily. Latitude at noon 0° 10' 30" N. Ship's run from 
sight to noon N 79° E (true) 31 miles. 



Dip 



R. &P. 



Chron. 27d 
Fast 


21h 33' 10" 
- 03' 28" 


36.8 ( 
4".7 

173" 

Dec. 27d 20h 
Corr. 1.5h 

Dec. 27d 21.5h 


lays 


Ace. Rate 


21h 29' 42" 
+ 02' 53" 


Ace. Rate 

21° 08'.8 S 
T- 0'.7 


G.M.T. 
Eq. Time 


21h 32' 35" 
+ 12' 16" 


21° 09.'5 S 
90° 00' 


G. A. T. 27d 


21h 44' 51" 






P.D. 


111° 09'.5 






Lat. at Noon 
Diff. Lat. 

Lat. at Sight 


00° 10' 30" N 
5' 54" S 




00° 04' 56" N 






Dep. 30.4 miles; 


; Diff. Long. 30'.4. 


Obs. Alt. 
S. D. 


50° 25' 00" 
+ 16' 12" 







50° 41' 12" 
5' 22" 

50° 35' 50" 
42" 



h 

Lat. 

P.D. 


50° 35' 

0° 04' 

111° 09' 


08" 
36" 
30" 


Sec 
Csc 

Cos 
Sin 

Log. 


Hav. 

21h 43' 
21h44' 


59" 
51" 


or 
W 
E 

E 


.00000 
.03031 


s 
s-h 


2)161° 49' 
80° 54' 
30° 19' 

L. A. T. 27d 
G. A. T. 27d 

Long, at Sight 

Diff. Long. 

Long, at Noon 


14" 
37" 
29" 


9.19862 
9.70300 




8.93193 




0° 13' 
30' 


52" 
00" 
24" 






0° 17' 


24" 





160 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

PROBLEM NO. 9 

Mar. 21, 1919, P. M. Obs. Alt. Sun's L. L. 34° 17' 30". Dip 36 ft. 
Chronometer read 9h 45' 17" A. M., which was fast on Feb. 27th, Ih 06', 
and losing 9. "5 daily. Latitude at noon 23° 15' S. Ship's run from noon 
to sight N 24° W (true) 56 miles. 



Chron. 
Fast 


I 

L. 

G. 

Lc 
D] 
Lc 


21h 45' 17" 
- Ih 06' 00" 


Dec. 20 

Corr. .'3 

Dec. 20 

P.D. 

Lat. at 
Diff. U 

Lat. at 

Dep. 
25' E. 

Sec 
Csc 

Cos 
Sin 

Log 


21.8 c 
9."5 

207" 

d20h 
'h 

d 20.7h 

Noon 
it. 

Sight 

22.8 m 

Hrv. 

3h 29' 
20h 35' 


lays 

Ace. Re 
0° 




Ace. Rate 


20h 39' 17" 
+ 3' 27" 


ite 

08' .2 S 

.7 


G. M. T. 20d 
Eq. Time 


20h 42' 44" 
7' 34" 


0° 
90° 


07'.5 S 
00' 


G. A. T. 20d 


20h 35' ] 

34° 17' 

+ 16' 


LO" 

30" 
06" 




89° 
23° 


52'.5 

15' 00" S 
51' 12" N 


Obs. Alt. 
S D. 


22° 
iles; I 

25" 
10" 


23' 48" S 
)iff. Long. 


Dip 


34° 33' 
- 5' 


36" 
53" 




R. &P. 


34° 27' 
- 1' 


43" 
17" 




h 

Lat. 

P.D. 


34° 26' 

22° 23' 
89° 52' 


26" 
48" 
30" 


.03406 
0.0000 


s 
s-b 


2)146° 42' 
73° 21' 
38° 54' 

A. T. 21d 
A. T. 20d 

)ng. at Sight 

ff. Long. 

>ng. at Noon 


44" 
22" 
56" 


9.45700 
9.79808 




9.28914 




6h 54' 

103° 33' 

25' 


15" or 

45" E 

E 






103° 58' 


45" E 





SIMPLE RULES AND PROBLEMS IN NAVIGATION 161 

PROBLEM NO. 10 

Sept. 30, 1919, A. M. Obs. Alt. Sun's L. L. 38° 16' 45". Dip 24 ft. 
Chronometer read llh 17' 25" P. M., which was fast on Aug. 28th, 2h 15', 
and gaining 4". 7 daily. Latitude at noon 41° 16' N. Ship's run from 
sight to noon S 84° W (true) 63 miles. 



Chron. 
Fast 


llh 17' 25" 
- 2h 15' 


33.- 

4' 

157 

Lat. at Noon 
Diff. Lat. 

Lat. at Sight 

Dep. 62.7 
83' W. 

Dec. 30d 8h 
Corr. Ih 

Dec. 30d 9h 
P.D. 


4 days 
'.7 


Ace. Rate 


9h 02' 25" 
2' 37" 


'" Ace. Rate 

41° 16' 00" N 
06' 36" N 


G. M. T. 30d 
Eq. Time 


8h 59' 48" 
+ 9' 49" 


41° 22' 36" N 
miles; Diff. Long. 

2° 37'.3 S 
l.'O 


G. A. T. 30d 


9h 09' 37" 

38° 16' 46" 
+ 16' 00" 




2° 38'.3 
90° OO'.O 


Obs. Alt. 
S. D. 


92° 38'.3 



38° 


32' 

4' 


46" 

48" 


38° 


27' 

r 


57" 
07" 


38° 
41° 
92° 


26' 
22' 
38' 


50" 
36" 
18" 


2)172° 


27' 


44" 



Dip 



R. &P. 

h 

Lat. 41° 22' 36" Sec .12472 

P.D. 92° 38' 18" Csc .00046 



s 86° 13' 52" Cos 8.81780 

s-h 47° 47' 02' Sin 9.86959 



Log. Hav. 8.81257 



L. A. T. 29d 22h 01' 53" 

G. A. T. 30d 9h 09' 37" 



Long, at Sight llh 07' 44" or 

166° 56' 00" W 
Diff. Long. 1° 23' 00" W 



Long, at Noon 168° 19' 00'' W 



CHAPTER XI 
DEVIATION BY AZIMUTH OF SUN 

This problem is to find error and deviation of the com- 
pass. 

Azimuth is the true bearing of a heavenly body and is 
reckoned from the north point in north latitude and from 
the south point in south latitude from 0° to 180°. 

For example, if in north latitude and the sun bore N 
80° E the azimuth would read N 80° E, if it bore S 80° E, 
the azimuth would be N 100° E. 

The azimuth is obtained by a shadow pin at the center 
of the compass or sight vanes which cast shadow lines across 
the compass. Due to difficulty of reading caused by rolling, 
pitching, etc., several readings should be taken and the 
average used. In practice azimuths are read to the nearest 
degree. 

Since azimuth is changing rapidly close to noon, azimuth 
of the sun should be taken in the morning or the evening 
when azimuth is changing slowly. 

TIME AZIMUTH 

if azimuth is taken at least two hours before, or after 
noon, it is sufficient to know apparent time of the ship to 
nearest minute. If chronometer is read to nearest one-half 
minute, and equation of time and longitude in time found 
with some degree of accuracy it will be sufficiently close to 
obtain from the H. O. 71 tables, the true bearing to the 
nearest degree. 

Place compass bearing and true bearing under each 
other, and the difference will be the compass error. 

Name the error as follows : 

If the true bearing is to right of compass bearing, error 
is east. 

If the true bearing is to left of compass bearing, error 
is west. 

Note. — Always imagine that you are standing in the 
center of the compass and looking toward the bearings. 

162 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 163 



Under the error put down the variation as given in 
example and apply as follows : 

Variation and error same name, subtract lesser from 
greater. 

Variation and error different name, add the two. 

The result will be deviation of compass on course steered 
at time of taking the bearing. 

Name the deviation as follows : 

The deviation will always be named the same as the 
error, unless you subtract the error from the variation; it 
will then be named the opposite name to error. 



July 5, 1919. 
Long. 62° 10' W. 

G. M. T. 4d 
Eq. Time 

G. A. T. 

Long. 

L. A. T. 4d 

True Bearing 
Compass Bearing 

Error 
Variation 



PROBLEM NO. 1 

Chronometer read llh 16' 30" A. M. Lat. 18° S. 
Sun bore by compass N 70° E. Variation 6° E. 

23h 16'.0 In July declination is N or oppo- 

— 4'.0 site name to latitude. 



23h 12'.0 

4h 08'.7 

19h 03'.3 

S 117° E 
S 110° E 



7° W 
6° E 



Deviation 



13° W 



PROBLEM NO. 2 

Oct. 24, 1919. Chronometer read 3h 23'.5 A. M. Lat 40° N. Long. 
91° 02' E. Sun bore by compass N 135° E. Variation 41° E. 

G. M. T. 23d 15h 23'.5 In October decimation is S, or 

Eq. Time + 15'.5 opposite name to latitude. 



G. A. T. 23d 

Long. 

L. A. T. 



15h 39'.0 
6h 04'.0 

21h 43' or 
9:43 A.M. 



True Bearing 
Compass Bearing 

Error 
Variation 

Deviation 



N 140° 


E 


N 


135° 


E 




5° 


E 




41° 


E 



36° W 



164 SIMPLE RULES AND PROBLEMS IN NAVIGATION 





PROBLEM NO. 3 




Jan. 30, 1919. Chronometer read Ih 50' P. M. Lat. 28° N, 
91° 15' W. Sun bore by compass N 126° E. Variation 7° E. 


Long. 


G. M. T. 30d 
Eq. Time 


Ih 50' 
13' 


In Januarj^ decHnation i 
opposite name to latitude. 


is S, or 


G. A. T., 30d 
Long. 


Ih 37' 
6h 05' 




L. A. T. 29d 

30d 


19h 32' or 
7:32 A.M. 




True Bearing 
Compass Bearing 


N 117° E 
N 126° E 






Error 
Variation 


9° W 
7° E 




Deviation 


16° W 






PROBLEM NO. 4 




Apr. 19, 1919. Chronometer read Ih 02' A. M. Lat. 36° N. 
110° 25' E. Sun bore by compass N 103° E. Variation 6° E. 


Long. 


G. M. T. 18d 

Eq. Time 


13h 02' 
+ 0'.5 


In April declination is N, 
name as latitude. 


or same 


G. A. T. 

Long. 


13h 02'.5 
7h 21'.5 




L. A. T. ISd 


20h 24' or 

8:24 A.M. 




True Bearing 
Compass Bearing 


N 103° E 
N 103° E 






Error 
Variation 


0° 
6° E 




Deviation 


6° W 





CHAPTER XII 
DEVIATION BY AMPLITUDE 

An amplitude is the bearing of a heavenly body at rising 
or setting. 

It is reckoned from the East and West points of the com- 
pass toward North and South from 0° to 90°. 

East and West are reckoned as 0° and North and South 
as 90°. 

To convert a compass bearing into an amplitude pro- 
ceed as follows: 

If the sun bore at rising N 82° E, the compass amplitude 
would be E 8° N. 

If the sun bore at setting S 79° W, the compass amplitude 
would be W 11° S. 

Put down chronometer time and correct fast or slow as 
given. 

Answer will be Greenwich Mean Time. 

Take out Sun's declination for Greenwich date and time 
for degree and nearest minute. 

From Table 44 (Bowditch) take out the following logs: 

Secant of latitude. Rejecting 10 from index number. 

Sine of declination. 

Add these two logs together. 

Look for Sine (Table 44) that agrees with sum of logs, 
and the degrees and minutes from top and side of page will 
be true amplitude. 

Name the true amplitude as follows: 

If sun is rising, name it East. If declination is North, 
name N, if South, name S. 

If sun is setting name it West. If declination is North, 
name N, if South, name S. 

Now convert compass bearing into an amplitude, and 
apply it to true amplitude as follows: 

165 



166 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

If both are of same name, subtract less from greater. 

If different names, add the two. 

Result will be error of compass. 

Name the error of compass as follows : 

If true bearing is to right of compass bearing, the error 
is East. 

If true bearing is to left of compass bearing, the error is 
West. 

Always imagine yourself standing in the center of the 
compass, and looking towards the bearings. 

Under the error put down the variation given in example, 
and apply as follows : 

Variation and error same name, subtract less from 
greater. 

Variation and error different name, add the two. 

Answer will be deviation. 

Name the deviation as follows : 

The deviation will always be named the same as the 
error, unless you subtract the error from the variation, it 
will then be named the opposite name to error. 

Table 39 (Bowditch) may also be used. Most local 
inspectors, however, insist that the amplitude be worked out. 



PROBLEM NO. 1 

Jan. 30, 1919. Sun bore at rising N 83° E. Chronom- 
eter read 2h 12' P.M. Lat. 46° 15' S. Variation 8° E. 

G.M.T 30d 2h 12' Dec. 30d 2h 17° 51' S 



Sec. of Lat. 
Sin of Dec. 


.16020 
9.48647 


Sin 

True Amp. 
Compass Amp. 


9.64667 

E 26° S 

E 7° N 


Error 
Variation 


33° E 

8° E 


Deviation 


25° E 



Check by Table 39 for Lat. 46° S; dec. 18° S; amp. E 
26° S. 



9.42316 

E 15° S 
E 19° S 


4 
25 


° W 

° w 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 167 



PROBLEM NO. 2 

Oct. 22, 1919. Sun bore at rising S 71° E. Chronometer 
read Ih 50' P. M. Lat. 43° 02'N Variation 25° W. 

G. M. T 22d Ih 50 Dec. 11° 10' S 

Sec. of Lat. .13611 

Sin of Dec. 9.28705 

Sin 

True Amp. 
Compass Amp. 

Error 
Variation 

Deviation 21° E 

Check by Table 39 for Lat. 43° N; dec. 11° S; amp. E 
15° S. 



PROBLEM NO. 3 

Apr. 19, 1919. Sun bore at setting S 82° W. Chronom- 
eter read 9h 15' A. M. Lat. 40° 12' N. Variation 6° E. 

G. M. T. 18d 21h 15' Dec. 10° 52' N 

Sec. of Lat. .11702 

Sin of Dec. 9.27537 

Sin 

True Amp. 
Compass Amp. 

Error 
Variation 

Deviation 16° E 

Check by Table 39 for Lat. 40° N; dec. 11° N; amp. 14^ 



9.39239 

W 14° N 

W 8° S 


22° E 
6° E 



168 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 4 

Mar. 11, 1919. Sun bore at rising S 88° E. Chronometer 
read 8h 15' A. M. Lat. 0° lO'N. Variation 15° E. 

G. M. T. lOd 20h 15' Dec. 4° 05' S. 

Dec. =True Amp. in Lat. 0° 



True Amp. 
Compass Amp. 


E 4° S 
E 2° S 


Error 
Variation 


2° E 
15° E 


Deviation 


13° W 



PROBLEM NO. 5 

Sept. 23, 1919. Sun bore at setting N 79° W. Chro- 
nometer read 2h 10' P. M. Lat. 48° N. Variation 2° W. 

G. M. T. 23d 2h 10' Dec. 0° 12' N 

True Amp. is E or W or 0° in Dec. 0°. 



True Amp. 
Compass Amp. 


W 0° 
W 11° N 


Error 
Variation 


11° W 

2° W 


Deviation 


9° W 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 169 

PROBLEM NO. 6 

Aug. 11, 1919. Sun bore at setting S 81° W. Chro- 
nometer read lOh 28' A. M., slow 32'. Lat. 18° 28' S. Vari- 
ation 30° E. 



Chronometer 22h 28' 
Slow + 32' 




G.M.T.lOd 23h 00' 

Sec. of Lat. 
Sin of Dec. 


Dec. 15° 33' N 

.02296 
9.42826 


Sin 

True Amp. 
Compass. Amp. 


9.45122 

W 16° N 
W 9° S 


Error 
Variation 


25° E 
30° E 


Deviation 


5° W 



Check by Table 39 for Lat. 18° S; dec. 15°.5 N; amp. 
W 16° N. 

PROBLEM NO. 7 

Jan. 31, 1919. Sun bore at rising S 84° E. Chro- 
nometeter read 4h 16' P.M. Lat. 36° 18' N. Variation 
3°W. 



G. M. T. 31d 4h 16' 

Sec. of Lat. 
Sin of Dec. 


Dec. 17° 33' S. 

.09370 
9.47934 


Sin 

True Amp. 
Compass Amp. 


9.57304 

E 22° S 
E 06° S 


Error 
Variation 


16° E 
3° W 


Deviation 


19° E 



Check by Table 39 for Lat. 36° N; dec. 17°.5 S; amp. 

E 22° S. 



170 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 8 

July 4, 1919. Sun bore at setting S 84° W. Chro- 
nometer read llh 18' P. M., slow 40'. Lat. 36° 18' N. Vari- 
ation 10° W, 



Chronometei 
Slow 


: llh 18' 
+ 40' 




G.M.T.4d 


llh 58' 

Sec. of Lat. 
Sin Dee. 

Sin 

True Amp. 
Compass Amp. 

Error 
Variation 

Deviation 


Dec. 22° 54' N 

.09370 
9.59039 




9.68409 

W 29° N 
W 6° S 




35° E 
10° W 




45° E 



PROBLEM NO. 9 

Dec. 16, 1919. Sun bore at rising S 60° E. Chro- 
nometer read 2h 46' A. M., fast 34'. Lat. 0° 18' S. Vari- 
ation 10° W. 

Chronometer 14h 46' 
Fast - 34' 



G. M. T. 15d 14h 12' Dec 23° 16' S 

True Amp. E 23° S 

Compass Amp. E 30° S 



Error 7° W 

Variation 10° W 



Deviation 3° E 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 171 



PROBLEM NO. 10 

Mar. 21, 1919. Sun bore at setting N 78° W. Chro- 
nometer read lOh 36' P. M., fast 30'. Lat. 0° 14' N. Varia- 
tion 3° E. 

Chronometer lOh 36' 
Fast - 30' 



G. M. T. 21d lOh 6" Dec. 0° 06' N 

True Amp. 0° 00' 

Compass Amp. W 12° N 



Error 12° W 

Variation 3° E 



Deviation 15° W 



PROBLEM NO. 11 

Jan. 31, 1919. Sun bore at rising N 89° E. Chro- 
nometer read Ih 50' A. M. Lat. 41° 21' N. Variation 35° E. 

G. M. T. 30d 13h 50' Dec. 17° 42' S 

Sec. of Lat. .12454 

Sin of Dec. 9.48292 

Sin 

True Amp. 
Compass Amp. 

Error 
Variation 

Deviation 10° W 



9.60746 

E 24° S 

E 1° N 


25° 
35° 


E 
E 



172 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 12 

Oct. 23, 1919. Sun bore at setting S 88° W. Chro- 
nometer read 2h 10' P. M. Lat. 18° 24' N. Variation 
3° E. 

G. M. T. 23d 2h 10' Dec 11° 10' S 

Sec. of Lat. .02279 

Sin of Dec. 9.28705 

Sin 



True Amp. 
Compass Amp. 

Error 
Variation 



Deviation 13° W 



9.30984 

W 12° S 
W 2° S 


10° 
3° 


W 
E 



CHAPTER XIII 
LATITUDE BY POLARIS 

The latitude by Polaris (or North Star) can be obtained 
at any time the star is visible, as long as the sea horizon is 
clear enough to obtain a proper altitude. 

If the North Star were exactly at the pole, its altitude 
would be the latitude. It is, however, not quite at the pole; 
so that it apparently describes a small circle in the sky 
about the pole as an axis. This makes necessary a small 
correction to the true altitude; these corrections are given 
in the Nautical Almanac, Table 1, for every ten minutes 
Local Siderial Time. 

To find Local Siderial Time, add to the L. M. T. the 
Right Ascension of the Mean Sun at Greenwich Mean Noon, 
add correction to R. A. M. S. for time past Greenwich 
Mean Noon from bottom of pages 2-3, N. A. 

PROBLEM NO. 1 

Jan. 31, 1919, A. M. Obs. Alt. *Polaris 24° 55'. Dip. 36 tt. Chro- 
nometer read Oh 22' 00" P. M. Long. 93° 30' W. 

G. M. T. 31d Oh 22' 00" Obs. Alt. 24° 55' 00" 

Long. 6h 14' 00" Dip - 5' 53" 



L. M. T. 30d 18h 08' 00" 24° 49' 07" 

R.A.M.S.for31d 20h 38' 38" Ref. - 2' 05" 

Corr. for 22' 04" 



True Alt. 24° 47' 02" 

L. S. T. 30d 38h 46' 42" or Corr. (I. N. A.) + 1° 03' 48" 

14h 46' 42" 



Lat. 25° 50' 50" N 

PROBLEM NO. 2 

Jan. 30, 1919, A. M. Obs. Alt. *Polaris 27° 27'. Dip 36 ft. Chro-^ 
nometer read Oh 17' 00" P. M. Long. 90° W. 

G. M. T. 30d Oh 17' 00" Obs. Alt. 27° 27' 00" 

Long. 6h 00' 00" Dip - 5' 53" 



L. M. T. 29d 18h 17' 00" 27° 21' 07' 
R.A.M.S.for30d 20h 34' 41" Ref. - 1' 52' 
Corr. for 17' 3" 



True Alt. 27° 19' 15" 

L. S. T. 38h 51' 44" or Corr. (L N. A.) + 1° 03' 18" 

14h52' 



Lat. 28° 22' 33" N 

173 



174 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 3 

July 15, 1919, P. M. Obs. Alt. *Polaris 26° 17'. Dip 20 ft. Chro- 
nometer read Ih 15' 21" P. M. Long. 82° 17' E. 



G. M. T. 15d 

Long. 


Ih 15' 21" 
5h 29' 08" 


Obs. Alt. 
Corr. (46) 

True Alt. 
Corr. (I. N. A.) 

Lat. 


26° 17' 00" 
6' 21" 


L. M. T. 
R. A. M. S. 
Corr. for Ih 15' 


6h 44' 29" 

7h 29' 09" 

0' 11" 


26° 10' 39" 
+ 1° 06' 12" 


27° 16' 51" N 


L. S. T. 


14h 13' 49" or 
14hl4' 



PROBLEM NO. 4 

Nov. 10, 1919, A. M. Obs. Alt. *Polaris 36° 21'. Dip 17 ft. Chro- 
nometer read llh 15' 20" A. M. Long. 98° 22' W. 

G. M. T. 9d 23h 15' 20" Obs. Alt. 36° 21' 00" 

Long. 6h 33' 28" Corr. (46) - 5' 21" 



16h 41' 

15h 10' 

3' 


52" 
26" 
49" 



L. M. T. 16h 41' 52" True Alt. 36° 15' 39" 

R. A. M. S. 9d 15h 10' 26" Corr. (I. N. A.) + 7' 42" 

Corr. for 23h 15' 



L.S.T. 31h 56' 07" or 

7h56' 



Lat. 36° 23' 21" N 



PROBLEM NO. 6 



Aug. 6, 1919, A. M. Obs. Alt. *Polaris 28° 16'. Dip 23 ft. Chro- 
nometer read 2h 16' 28" A. M., slow 1' 25". Long. 38° 21' E. 

Chron. 5d 14h 16' 28" Obs. Alt. 28° 16' 00" 

Slow -h 1' 25" Dip - 4' 42" 

G. M. T. 

Long. 2h 33' 24" Ref. 



14h 17' 
2h33' 


53" 
24" 


16h 51' 

8h51' 

2' 


17" 
57" 
21" 



L. M. T. 16h 51' 17" True Alt. 

R. A. M. S. 5d 8h 51' 57" Corr. (I. N. A.) 



Corr. 14h 16' 



L. S. T. 25h 45' 35" or 

lh46' 



28° 11' 
1' 


18" 
49" 


28° 09' 
1° 07' 


29" 
12" 



Lat. 27° 02' 17" N 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 175 



PROBLEM NO. 6 

June 8, 1919, A. M. Obs. Alt. *Polaris 23° 12' 15". Dip 38 ft. 
Chronometer read llh 55' 25" A. M. Long. 110° 15' W. 

G. M. T. 7d 23h 55' 25" Obs. Alt. 23° 12' 15" 

Long. 7h 21' 00" Dip - 6' 02" 

L. M. T. 7d 16h 34' 25" 

R. A. M. S. 4h 59' 20" Ref. 

Corr. for 23h 55' 3' 56" 

True Alt. 

L. S. T. 21h 37' 41" Corr. (I. N. A.) 

Lat. 22° 29' 09" N 



PROBLEM NO. 7 

May 20, 1919, P. M. Obs. Alt. *Polaris 42° 16' 30". Dip 39 ft. 
Chronometer read 6h 16' 23", fast 3' 18". Long. 3° 15' E. 

Chron. 6h 16' 23" Obs. Alt. 42° 16' 30" 

Fast - 3' 18" Dip - 6' 07" 



23° 06' 

2' 


13" 
16" 


23° 03' 
34' 


57" 
48" 



G. M. T. 20d 6h 13' 05" 42° 10' 23" 

Long. + 13' 00" Ref. - 1' 04" 



6h 13' 
13' 


05" 
00" 


6h26' 

3h48' 

1' 


05" 
22" 
01" 



L. M. T. 6h 26' 05" True Alt. 42° 09' 19' 

R. A. M. S. 20d 3h 48' 22" Corr. (I. N. A.) + 44' 24' 
Corr. 6h 13' 

L. S. T, lOh 15' 28 



Lat. 42° 53' 43" N 



PROBLEM NO. 8 

Oct. 6, 1919, A. M. Obs. Alt. *Polaris 50° 24' 45". Dip 40 ft. 
Chronometer read 9h 22' 03" A. M., slow 4' 23". Long. 18° 16' W. 



Chron. 
Slow 


9h 22' 03" 
+ 4' 23" 


Obs. Alt. 
Dip 

Ref. 

True Alt 
Corr. (I. 

Lat. 


N. 


A.) 


50° 24' 45" 
6' 12" 


G. M. T. 5d 

Long. 


21h 26' 26" 
Ih 13' 04" 


60° 18' 33" 

- 48" 


L. M. T. 

R. A. M. S. 5d 

Corr 


20h 13' 22" 

12h 52' 25" 

3' 31" 


50° 17' 45" 

+ 28' 12" 




60° 45' 57" N 


L. S. T. 


33h 09' 18" or 
9h 09' 



176 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 9 

Feb. 12, 1919, A. M. Obs. Alt. *Polaris 48° 16'. Dip 21 ft. Chro- 
nometer read 2h 06' 28" P. M. Long. 152° W. 

G. M. T. 12d 2h 06' 08 ' Obs. Alt. 48° 16' 00" 

Long. lOh 08' 00" Dip - 4' 29" 



L. 


M, 


. T. 




15h 58' 


28" 


R. 


A. 


M.S. 


12d 


21h 25' 


50" 


Corr. 


2h06' 






21" 



48° 11' 31' 
Ref. - 52' 



True Alt. 48° 10' 39' 

L. S. T. 37h 24' 45" or Corr. (I. N. A.) + 1° 07' 12' 

13h 25' 



Lat. 49° 17' 51" N 



PROBLEM NO. 10 

June 6, 1919, P. M Obs. Alt. *Polaris 29° 41' Dip 20 ft. Chro- 
nometer read 8h 16' 21" A. M. Long. 161° 15' E. 



G. M. T. 5d 
Long. 


20h 16' 21" 
lOh 45' 00" 


Obs. Alt. 
Dip 

Ref. 

True Alt. 
Corr. (I. N. A.) 

Lat. 


29° 41' 00" 
- 4' 23" 


L. M. T. 6d 
R A. M. S. 5d 
Corr. 20h 16' 


7h 01' 21" 

4h 51' 27" 

3' 20" 


29° 36' 37" 
- 1' 42" 


29° 34' 55" 
+ 1° 01' 36" 


L. S. T. 


llh 56' 08" 




30° 36' 31" N 



PROBLEM NO. 11 

Oct. 25, 1919, A. M. Obs. Alt. *Polaris 47° 15'. Dip 26 ft. Chro- 
nometer read Ih 16' 28" P. M. Long. 100° W. 



G, M. T. 25d 
Long. 


Ih 16' 28" 
6h 40' 00" 


Alt. 
Dip 

Ref. 

True Alt. 
Corr. (I. N. A.) 

Lat. 


47° 15' 00" 
5' 00" 


L. M. T. 

R. A. M. S. 25d 

Corr. Ih 16' 


18h 36' 28" 

14h 11' 18" 

12" 


47° 10' 00" 
- 54" 


47° 09' 06" 
+ 22' 30" 


L. S. T. 


8h 47' 58" 




47° 31' 36" N 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 177 



PROBLEM NO. 12 

July 4, 1919, A. M. Obs. Alt. *Polaris 28° 32' 00". Dip 27 ft. Chro- 
nometer read lOh 58' 03" A. M. Long. 94° 50' W. 



G. M. T. 3d 
Long. 


22h 58' 03" 
6h 19' 20" 


Alt. 
Dip 

Ref. 

Corr. 
Corr. 

Lat. 


Alt. 

(I.N. 


A.) 


28° 32' 00^' 
- 5' 06" 


L. M. T. 

R. A. M. S. 3d 
Corr. 22h 58' 


16h 38' 43" 

6h 41' 51" 

3' 46" 


28° 26' 54" 
- 1' 47" 


28° 25' 07" 
56' 54" 


L. S. T. 


23h 24' 20" 




27° 28' 13" N 



PROBLEM NO. 13 

Feb. 12, 1919, P. M. Obs. Alt. *Polaris 26° 12' 00". Dip 14 ft. 
Chronometer read 7h 23' 15" A. M. Long. 175° E. 

G. M. T. lid 19h 23' 15" Obs. Alt. 26° 12' 00" 

Long. llh 40' 00" Dip - 3' 40" 



Ref. 

True Alt. 
Corr. (I. N. A.) 
L. S. T. 28h 28' 26" 

4h 28' Lat, 25° 18' 16" N 



PROBLEM NO. 14 

Apr. 10, 1919, A. M. Obs. Alt. *Polaris 13° 16'. Dip 18 ft. Chro. 
nometer read Oh 02' 23" A. M., fast 5' 12". Long. 81° 15' E. 

Chron. 9d 12h 02' 23" Obs. Alt. 13° 16' 00" 

Fast - 5' 12" Dip - 4' 09" 



L. M. T. lid 


31h 03' 


15" or 


12d 


7h03' 


15" 


R. A. M. S. lid 


21h 22' 


00" 


Corr. 19h 23' 


3' 


11" 



26° 


08' 


20" 




1' 


58" 


26° 


06' 


22" 




48' 


06" 



G. M. T llh 57' 11" 13° ir 51' 

Long. 5h 25' 00" Ref. - 4' 04' 



L. M. T. 17h 22' 11" True Alt. 13° 07' 47' 
R. A. M. S. 9d Ih 06' 43" Corr. (I. N. A.) 4- 18' 18' 
Corr. llh 57' V 58" 



L. S. T. 18h 30' 52' 



Lat. 13° 26' 05" N 



CHAPTER XIV 

LONGITUDE BY SUN, ALTITUDE AZIMUTH, 

MERIDIAN ALTITUDE OF SUN AND 

MERCATOR SAILING COMBINED 

This problem is worked the same as previous methods 
for obtaining latitude by sun, longitude by sun, and course 
and distance by Mercator's Sailing. 

The difference in the chronometer sights are that two 
rates for the chronometer are given, and it is necessary to 
find the daily rate. 

To find daily rate of chronometer proceed as follows: 

If first and second rate are both fast or both slow, sub- 
tract less from greater. 

If first and second rate are one fast and one slow, add the 
two. 

Turn this result to seconds, by multiplying minutes by 
60 and add to the result the seconds. 

Divide number of seconds by number of days between 
the rates, and the result will be Daily Rate. 

Put down chronometer time and apply to it the last rate 
given in example. 

Find the number of days between last rate and date of 
example to the nearest tenth of a day, and multiply number 
of days and tenths by Daily Rate already obtained. 

Result will be Accumulated Rate, which apply to 
chronometer, and the result will be G. M. T. 

The latitude at noon is found if sun's meridian altitude 
is given, and latitude at sight found as in previous noon 
position sights. 

Now proceed to find the longitude at sight and noon. 

The altitude azimuth is worked in conjunction with a 
regular longitude by sun sight, and the sun's true bearing is 
obtained without the use of azimuth tables. 

To find sun's true bearing by altitude azimuth proceed 
as follows: 

Add together true altitude, latitude and polar distance, 
using the same altitude, latitude and polar distance that 
longitude sight was worked with. 

178 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 179 

Divide sum by 2, answer will be Half Sum. 

Under Half Sum put down polar distance, and subtract 
less from greater, result will be Remainder. 

From Table 44 (Bowditch) take out the following logs: 

Secant of Altitude. Rejecting 10 from index number. 

Secant of latitude. Rejecting 10 from index number. 

Cosine of Half Sum. 

Cosine of Remainder. 

Add these four logarithms together. 

Log. Haversine (Table 45) gives azimuth. Result will 
be sun's true bearing from depressed pole. 

If in north latitude name the true bearing S. If sight is 
A. M. East, P. M. West. 

If in south latitude name the true bearing N. If sight 
is A. M. East, P. M. West. 

Under true bearing put down compass bearing and 
obtain error and deviation of compass same as in azimuths 
from the tables. 

The position of the ship at noon is then put down as 
Lat. A and Long. A, and the course and distance found by 
Mercator's Sailing to position given in example. 

PROBLEM NO. 1 

Jan. 31, 1919, A. M. at ship. Obs. Alt. Sun's L. L. 35° 28' 18". 
Dip 15 ft. I. E. +50". Chronometer read 2h 30' 44", which was 
slow on Nov. 25, 10' 20", and on Dec. 11 was slow 13' 49". Observed 
Meridian Altitude of Sun's L. L. at noon was 59° 59' S. D. R. long. 
87° W. Ship ran from sight to noon S 73° W. (true) 48 miles. Sun bore 
by compass N 108° 15' E. Variation 16° W. 

Required position at sight and noon; error and deviation by altitude 
azimuth; also course and distance by Mercator's sailing from noon to 
7° 15' S., 125° 35' W. 

Obs. Mer. Alt. 59° 59' 00" S G. A. T. 31d 5h 48' 00" 

I. E. + 50" Eq. Time + 13' 31" 



59° 59' 50" G. M. T. 31d 6h 01' 31" or 
Corr. (46) + 11' 59" 31d 6h 



Dec. 17° 31'.4 S 



True Alt. 60° 11' 49" S 

90° 00' 00" Course, N 73° E; Distance 48 
miles; Diff. Lat., 14' N; Dep., 

Z. D. 29° 48' 10" N 45.9 miles E; Diff. Long., 46'.5 E. 

Dec. 17° 31' 24" S 



Slow, Nov. 25th 10' 20" 

Lat. at Noon 12° 16' 46" N Dec. 11th 13' 49" 
Diff. Lat. 14' 00" N 



3' 29' 



Lat. at Sight 12° 30' 46" N or losmg 209' 



180 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

209 -„,, , ., 
Chron. 2h 30' 44" le " claily rate. 

Slow 13' 49" 51 . 1 days intervaL 

^«^- ^^*® ^^' ^^" 664" = 11' 4" ace. rate losing. 



G. M. T. 31d 2h 55' 37" j^^^ 3^^ 2h 17° 34'.2 S 

Eq.Time - 13' 30" Corr. .9h 0'.6 



G. A. T. 31d 2h 42' 07" j^^^ g^^ 2.9 h 17° 33'.6 S 

Obs. Alt. 35° 28' 18" 

I. E. + 50" 

Corr. (46) 11' 16" 



True Alt. 35° 40' 24" Sec .09026 

Lat. 12° 30' 46" Sec .01044 Sec .01044 

P. D. 107° 33' 36" Csc .02072 

2 )155° 44' 46" 

One-half Sum 77° 52' 23" Cos 9 . 32239 Cos 9 . 32239 

One-half Sum Alt. 42° 11' 59" Sin 9.82719 

One-half Sum P. D. 29° 41' 13" Cos 9 . 93889 



Log. Hav. 9 . 18074 Log. Hav.9 . 36198 

True Bearing S 57° 20' E( 

N 122° 40' E 
Obs. Bearing N 108° 15' E 



L. A. T. 30d 20h 56' 40" True Bearing S 57° 20' Eor 

G. A. T. 31d 2h 42' 07" N 122° 40' E 



Long, at Sight 5h 45' 27" or 

86° 21' 45" W Error 14° 25' E 

Diff. Long. 46' 30"W Variation 16° 00' W 

Long, at Noon 87° 08' 15" W Deviation 30° 25' E 

Lat. A 12M7' N Mer. Parts 737.7 Long. A 87°08'W 

Lat. B 7° 15' S Mer. Parts 433.2 Long. B 125° 35' W 

Diff. Lat. 19° 32' or 1170.9 Diff. Long. 38° 27' or 

1172' 2307' 

Log. of Diff. Long. 2307 = 3 . 36305 
Log. of Mer. Parts 1171 = 3.06856 



Tan .29449= course S 63° 05' W 

Secant of Course 63° 05' .34420 
Log. Diff. Lat. 1172 3.06893 



Log. 3 . 41313 = distance 2589 miles. 

At Sight Lat. 12° 30' 46" N. Long. 86° 21' 45" W. 
At Noon Lat. 12° 16' 46" N. Long. 87° 08' 15" W. 
Compass Error 14° 25' E. Compass Deviation 30° 25' E. 
True Course S 63° 05' W, distance 2589 miles. 

It is interesting to check our azimuth, since the L. A. T. is known. 
H. 0. 71 may be used with apparent time of 8:57 A. M., Lat. 12°.5. and 
Dec. 17°.5. This gives to nearest degree N 123° E. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 181 



PROBLEM NO. 2 

Mar. 11, 1919, A, M. at ship. Obs. Alt. Sun's L. L. 23° 23'. Dip 38 ft. 
Chronometer read 3h 16' 28" A. M. which was fast on Jan. 1, 14' 28", and 
on Jan. 28 was slow 2' 12". Latitude at noon was 28° 17' S. Ship ran 
from sight to noon N 56° W (true) 49 miles. Required latitude and longi- 
tude at sight and noon. 

Sun bore by compass S 108° 16' E. Variation 14° W. Required error 
and deviation of compass by altitude azimuth. 

Required true course and distance made by Mercator's sailing from 
noon to Lat. 16° 12' S., Long. 15° 10' E. 

Chronometer 15h 16' 28" Chron., fast Jan. 1 14' 28" 

Slow 4- 2' 12" Slow, Jan. 28 2' 12" 



Ace. Rate + 25' 39' 



G. M. T. lOd 15h 44' 19" =1000" 

Eq. Time - 10' 28" 1000' 



Lost 16' 40' 

= 37" Daily Rate 



27d 

G. A. T. lOd 15h 33' 51" 41 . 6 Days Losing 

Dec. lOd 14h 4° lO'.O 1539" Ace. Rate = 25' 39' 

Corr. 1.7h - 1'.7 



Dec. 4° 08'.9 S or 

4° 08' 54" 
P. D. 85° 51' 06" 

Lat. at Noon 28° 17' S 

Diff. Lat. + 27'.4 S Course, S 56° E; Dist., 49 mHes; 

Diff. Lat., 27.4 miles; Dep., 40.6 

Lat. at Sight 28° 44',4 S miles; Diff. Long., 46'. 

Obs. Alt. 23° 23' 00" 

S. D. + 16' 06" 



23° 39' 06' 
Dip - 6' 02' 



23° 33' 04' 
R. & P. - 2' 05' 



True Alt. 
Lat. 
P. D. 


23° 30' 59" 

28° 44' 24" 
85° 51' 06" 


Sec 
Csc 

Cos 
Sin 


.05710 
.00114 

9.55326 
9.85352 


Sec 
Sec 

Cos 
Cos 


.03766 
.05710 


Half Sum 
s-Alt. 
s-P. D. 


2)138° 06' 29" 

69° 03' 14" 
45° 32' 15" 
16° 47' 52" 


9.55326 
9.98107 



Log. Hav. 9 . 46502 Log. Hav. 9 . 62909 



182 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

L. A. T. lOd 19h 38' 27" True Bearing N 81° 27' 15'' E or 

G. A. T. lOd 15h 33' 51" S 98° 33' E 



Obs. Bearing S 108° 16' E 

Long, at Sight 4h 04' 36" or 

61° 09' 00" E Error 9° 43' E 

Diff.Long. 46' W Variation 14° W 

Long. Noon 60° 23' 00" E Deviation 23° 43' E 

Lat. A 28° 17' S Mer. Parts. 1759.4 Long. A 60° 23' E 

Lat. B 16° 12' S Mer. Parts 978.7 Long. B 15° 10' E 



Diff. Lat. 725' 780.7 Diff.Long. 2713' 

Log. of Diff. Long. 2713' = 3 . 43345 
Log. of Mer. Parts. 780 . 7 = 2 . 89248 



Log. Tan . 54057 = course N 73° 56' Wo 

Log. Sec Course 73° 56' = . 55790 
Log. of Diff. Lat. 725' = 2 . 86034 



Log. 3 . 41824 = distance 2620 miles. 

At Sight Lat. 28° 44' 24" S, Long. 61° 09' 00" E. 
At Noon Lat. 28° 17' 00" S, Long. 60° 23' 00" E. 
Compass Error 9° 43' E. Compass Dev. 23° 43' E. 
True Course N 73° 56' W, distance 2620 miles. 

Entering H. 0. 71 with L. A. T. 7:38 A. M., Lat. 29°, Dec. 4° the azi- 
muth is found to be S 98°.5 E. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 183 



PROBLEM NO. 3 

Aug. 7, 1919, A. M. at ship. Obs. Alt. Sun's L. L. 18° 18'. Dip 32 ft. 
Chronometer read 5h 16' 28" P. M., which was fast on July 9, 4' 12", and 
on Aug. 4th was slow 3' 12". Latitude at noon 4° 16' N. Ship's run 
from sight to noon S 18° W. (true) 48 miles. 

Sun bore by compass N 92° E. Variation 28° W. 

Required latitude and longitude at sight and noon; error and deviation 
of compass by altitude azimuth ; and true course and distance from noon 
to Lat. 5° 28' S., Long. 150° E. 

Chron. 5h 16' 28" Chron., fast Jul. 9 4' 12" 

Slow + 3' 12" Aug. 4, slow 3' 12" 

Ace. Rate + 55" 



Lost 7' 24" or 



G. M. T. 7d 5h 20' 35" 444' 

Eq. Time - 5' 42" 444>" 



26d 



= 17'MRate Times 3.2 days 



G. A. T. 7d 5h 14' 53" =55" Lost 

Dec.7d4h 16° 36'.6 N 

Corr. 1.3h - 0'.9 



Dec. 16° 35'.7 N 

P. D. 73° 24'.3 

Lat. at Noon 4° 16' 00" N 

Diff. Lat. 45' 42" N Course, N 18° E; Distance, 48 

miles; Diff. Lat., 45.7 miles; Dep. 

Lat. at Sight 5° 01' 42" N 14.8 miles; Diff. Long., 15' W. 

Obs. Alt. 18° 18' 00" 

S. D. + 15' 48" 



18° 33' 48' 
Dip - 5' 33' 



18° 28' 15" 
R. & P. - 2' 44" 



True Alt. (h) 

Lat. 

P.D. 


18° 25' 31" 

5° 01' 42" 

73° 24' 18" 

2)96° 51' 31" 


Sec. 
Csc 


Sec 
.00167 Sec! 
.01848 


.02285 
.00167 


Half Sum (s) 

s-h 

s-p 


48° 25' 46" 
30° 00' 15" 
24° 58' 32" 


Cos 
Sm 


9.82187 Cos 
9.69902 

Cos 


9.82187 
9.95736 



Log. Hav. 9 . 54104 Log. Hav. 9 . 80375 



184 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

L. A. T. 6d 19h 11' 00" True Bearing S 105° 40' Eor 

G. A. T. 7d 5h 14' 53" N 74° E 



Obs. Bearing N 92° E 



Long, at Sight lOh 03' 53" or 

150° 58' 15" W Error 18° W 

Diff.Long. 15' W Variation 28° W 



Long. Noon 151° 13' 15" W Deviation 10° E 

Lat. A. 4° 16' N Mer. Parts 254.5 Long. A. 151° 13' W 

Lat. B 5° 28' S Mer. Parts 326.3 Long. B 150° 00' E 



Diff. Lat. 584' 580.8 Diff. Long. 3527' 

Log. of Diff . Long. 3527' = 3 . 54741 
Log. of Mer. Parts 580 . 8' = 2 . 76403 

Tan . 78338 = course S 80° 39' W. 

Log. Sec. Course 80° 39' = . 78924 
Log. Diff. Lat. 584' = 2 . 76641 



Log. 3 . 55565 = distance 3595 miles. 

At Sight Lat. 5° 01' 42" N, Long. 150° 58' 15" W. 
At noon Lat. 4° 16' 00" N, Long. 151° 13' 15" W. 
Compass Error 18° W. Compass Dev. 10° E. 
True Course S 80° 39' W, distance 3595 miles. 



CORRECTING LONGITUDE 

NOTE. — In practice it is common to work a morning time sight on 
D. R. latitude. When a noon sight is obtained, the latitude found at 
noon gives a more correct latitude for the A. M. sight. This correction 
to the latitude will affect the longitude. Either the entire calculation 
may be gone through again or the longitude previously found may be 
corrected by any of the following methods : 

(a) Using Table 38 (Bowditch), knowing altitude, latitude, and polar 
distance, the table gives the error due to 1' or mile error in latitude. 

(6) Using Table 47 (Bowditch), the sun's true bearing having been 
found for compass correction, and the approximate latitude kno\\Ti, the 
table gives the longitude factor or error in longitude produced by 1' or 
mile error in latitude. 

(c) Using Table 2 (Bowditch) using as a course 90° from the bearing 
find the departure corresponding to the error in the latitude column. 
The departure in miles is found with the middle latitude as course and the 
difference in longitude in minutes is found. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 185 



PROBLEM NO. 4 

Oct. 24, 1919, A. M. D. R. Lat. 22° 40' N. Obs. Alt. Sun's L. L. 
24° 16'. Dip 26 ft. Chronometer read 6h 23' 12" A. M., fast on Sept. 
25th, 8' 12", and on Oct. 20th, fast 6' 20". 

Sun bore by compass N 116° E. Variation 19° E. 

Ship's run from sight to noon N 43° W (true) 52 miles. 

Obs. Mer. Alt. was 55° 30' 00" S. 

Required true course and distance by Mercator SaiHng from noon to 
Lat. 0° 23' S, Long. 0° 23' W. 



Chron. 
Fast 


18h 23' 12" 
6' 20" 


Chron., fast Sep. 25 
Fast, Oct. 20 

Chron. Lost 

3.7 Days 

17" Losing 

Dec. 23d 18h 11° 
Corr. .3h + 


8' 12" 
6' 20" 


Ace. Rate 


18h 16' 52" 
+ 17" 


r 52" or 
112" 


G.M.T.23d 
Eq. Time 


18h 17' 09" 
{- 15' 35" 




G.A.T.23d 


18h 32' 44" 


23'.9 S 
0'.3 




Dec. 23d 18.3h 11° 
P. D. 101° 


24'.2 S 
24' 12" 



Obs. Alt. 
S. D. 



24'' 16' 00" 
+ 16' 06" 



Dip 


24° 32' 06" 
5' 00" 


R. &P. 


24° 27' 06" 
1' 59" 


True Alt. 
Lat. 
P. D. 


24° 25' 07" 

22^ 40' 00" 

101° 24' 12" 




2)148° 29' 19" 



s-h 
s-P. D. 



L. A. T. 23d 
G. A. T. 23d 



74° 14' 39" 
49° 49' 32" 
27° 09' 33" 



Sec 
Csc 

Cos 
Sin 



,03491 
,00866 



Sec 
Sec 



9.433S2 Cos 
9.88314 

Cos 



.04070 
.03491 



9.43382 
9.94926 



20h 11' 05' 

18h 32' 44' 



Long. 



Ih 38' 21" or 
24° 35' 15" E 



Log. Hav. 9.36053 Log. Hav. 9.45869 
True Bearing 

Obs. Bearing 



S 64° 51' 00" or 
N 115° 09' E 

N116° E 



Error 
Variation 

Deviation 



V 
19' 



20° 



W 
E 

W 



186 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



Course N 43* W. Dist. 52 miles. Diff. Lat. 38.0 miles. Dep. 35.5 
miles. Diff. Long. (Approx. Mid. Lat. 23^* N) 38.5'. 



Long, at Sight 
Diff. Long. 

Long, at Noon 



24* 35' 15" E 

38' 30" W 

23* 56' 45" or Ih 35' 47' 



G. A. T. (noon) 23d 22h 24' 13' 
Eq. Time - 15' 36' 



G. M. T. (noon) 23d 22h 08' 37' 

Obs. Alt. 
S.D. 



Dec. 23d 22h 
Corr. .Ih 

Dec. 

55* 30' 00" S 
+ 16' 06" 



11* 27'.4 S 
+ O'.l 

U* 27'.5 S 



Dip 

R.&P. 

True Alt. 
Z. D. 
Dec. 

Lat. (noon) 
Diff. Lat. 

Lat. at Sight 
Lat. Used 

Error 
Working time sight with new latitude. 



55° 


46' 06" 
5' 00" 


55° 


41' 06" 
0' 35" 


55° 
34° 
11° 


40' 31" S 
19' 29" N 
27' 30" S 


22° 


51' 59" N 

38' S 


22° 
22° 


13' 59" N 
40' 00" N 



26' 01" 



h 

Lat. 
P. D. 



s-h 



24° 25' 07' 

22° 13' 59' 

101° 24' 24' 

2 )148° 03' 30' 

74° or 45' 
49° 36' 38' 



Sec. 

Csc 



Cos 
Sin 



Log. Hav. 



.03355 

.00866 



9.43954 
9.88176 

9.36351 



L. A. T. (corr.) 
G. A. T. 

Long, (corr.) 



20h 10' 13" 

18h 32' 44" 

Ih 37' 29" 
Error 



or 



24° 22' 15" E 
24° 35' 15' E 



13' 



E 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 187 



TABLE 38 

Twenty-six miles error latitude, alt. 24°, Lat. 22*', P. D. 101^ 
Error in longitude for 1 mile latitude, . 5 
for 26 miles, 13 

Rule. — In east longitude, body east of meridian, decreased latitude, 
longitude is decreased. 



TABLE 47 

Bearing S 65° E (see calculations). 
Latitude 22°. 
Longitude factor F = .51. 
.51X26 miles = 13'. 



TABLE 2 

Bearing S 65° E. Find course 90° from it, or N 25'' E. Opposite 
Lat. 26°, find departure 12 miles. At Middle Lat. 22°, 12 miles = 13'. 

Noon position 22° 51' 59" N Long. Sight 

Diff. Long 

Long. Noon 
Lat. A 22° 52' N Mer. Parts 1400.9 Long. A 

Lat. B 0° 23' S Mer. Parts 22.8 Long. B 



24° 


22' 


15" 


E 




38' 


30" 


W 


23° 


43' 


45" 


E 




23° 


44' 


E 




0° 


23' W 



Diff. Lat. 23° i5' or 1424 Diff. Long. 24° 07' or 

1395' 1447' 

Log. of Diff. Long. 1447' » 3. 16047 

Log. of Mer. Parts 1424' =3. 15351 



Log. Tan. .00696- course S 45° 28' W 

Log. Sec. 45° 28' =0.15408 

Log. Diff. Lat. 1395' = 3 . 14457 



Log. 3 . 29865 « distance 1989 miles. 

Position at noon: Lat. 22° 52' N., Long. 23° 44' E. 
Position at sight: (corr.) 22° 14' N, 24° 22' E. 
Compass error 1° W, deviation 20^ W. 
True course S 45° W, distance 1989 miles. 



188 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 6 

Feb. 2, 1919, A. M. D. R. Lat. 36° 59' S. Obs. Alt. Sun's L. L. 
49° 10'. Dip 14 ft. Chron. read 7h 08' 50" A. M., slow on Dec. 30th, 
18' 02", and on Jan. 6th, slow 19' 10".6. 

Ship's run from sight to noon S 45° W (true) 32 miles. 

Sun bore by compass S 73° E. Variation 5° \V. 

Obs. Mer. Alt. 70° 25', bearing N. 

Required position and sight and at noon, also compass error and 
deviation. 

Required course and distance by Mercator Sailing from noon to Lat. 
riO'N, Long. 5°16'W. 



Chron. 
Slow 
Ace. Rate 


19h 08' 
+ 19' 
+ 4' 


50" 
10" 
22" 


Chron. slow Dec. 30th 
Chron. slow Jan. 6th 

Losing 

68" 6 

^^^'^= 9".8rate 

26.8 days 

Losing 262" = 4' 22" 

Dec. Id 18h 17° 
Corr. 1.5h 


18' 02" 
19' 10".6 


1' 08".6 
or 68".6 


G. M. T. Id 

Eq. Time 


19h 32' 
13' 


22" 
45" 


G. A. T. Id 


19h 18' 


37" 


06M 

or.o 




Dec. Id 19.5h 17° 
P. D. 72° 


05'.1 S 
54'.9 



Obs. Alt. 49° 10' 00' 

S D. + 16' 18' 





49° 


26' 


18" 










Dip 


- 


3' 


40" 












49° 


22' 


38" 




R. &P. 


- 




44" 






Sec 




True Alt. 


49° 


21' 


54" 


. 18626 


Lat. 


36° 


59' 


00" 


Sec 


.09756 Sec 


.09756 


P. D. 


72° 
2) 159° 


54' 
15' 


54" 

48" 


Csc 


.01960 






s 


79° 


37' 


54" 


Cos 


9.25521 Cos 


9.25521 


s-h 


30° 


16' 


00" 


Sin 


9.70245 






s-P.D. 


6° 


43' 


00" 






Cos 


9.99701 



Log, Hav. 9.07482 Log. Hav. 9.53604 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 189 



L. A. T. Id 
G. A. T. Id 


21h 18' 42" True Bearing 
19h 18' 37" Obs. Bearing 


N72°E 
S 73° E 


Long, at Sight 


2h GO' 05" or Error 
30° 01' 15" E Variation 

Deviation 


35° W 
5°W 




30° W 



Course S 45° W. Dist. 32 miles. Diff. Lat. 22.6 miles = 22.6 S. 
Dep. 22.6 miles (37° Mid. Lat.) =28' W. Long, at noon 29° 33' 15" E, or 
Ih 58' 13". 



G.A.T.ld 
Eq.Time 


22h 01' 47" Dec. Id 22h 17° 03'.3 S 
4- 13' 46" Corr. .3h 0'.2 


G. M. T. Id 

Obs. Alt. 
S.D. 


22h 15' 33" Dec. Id 22.3h 17° 03'.1 S 

70° 25' 00" N 
+ 16' 18" 


Dip 


70° 41' 18" 
- 3' 40" 


R.&P. 


70° 37' 38" 
17" 


Corr. Alt. 

Z.D. 

Dec. 


70° 37' 21" 

19° 22' 39" S 
17° 03' 06" S 


Noon Lat. 
Diff. Lat. 


36° 25' 45" S 

22' 36" N 


Lat. at Sight 36° 03' 09" S 
Lat. Used 36° 59' 00" S 



Error 55' 51" 

TABLE 47 
Lat. 37°. Bearing N 72° E; F = . 40. Long. Corr. = .40X55.8 = 22'.3. 



190 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

TABLE 2 

Course 18°. Lat. 55.8. Dep. 18.2 (Mid. Lat. 37°) Diff . Long. = 22'.7. 

Check on azimuth (H. O. 71) Lat. 37°. Dec. 17°. L. A. T. 9h 18'. 
Az. 108°. 

Long, at Sight (computed) 30° 01' 15" E 

Corr. (see above) 22' 18" dec. 



Long, at Sight (corrected) 
Diff. Long. 


29° 39' E 
28' W 


Long, at Noon (corrected) 


29° ir E 


Lat. A 36° 26' S Mer. Parts 
Lat. B 1° 10' N Mer. Parts 


2336 Long. A 29° 11' E 
69 Long. B 5° 16' W 


Diff. Lat. 37° 36' or 
2256' 


2405 Diff. Long 34° 27' or 
2067' 


Log. of Diff. Long. 2067'=3. 31534 
Log. of Mer. Parts 2405' = 3 . 38112 



Log. Tan. 9 . 93422 = course N 40° 41' W 

Log. Sec. Course = . 12015 

Log. of Diff. Lat. 2256' = 3 . 35334 



Log. I 3.47349 = distance 2975 mile 

Position at noon: Lat. 36° 26' S, Long. 29° 11' E. 
Position at sight: Lat. 36° 03' S, Long. 29° 39' E. 
Compass error 35° W. Dev. 30° W. 
True course N 41° W. Dist. 2975 miles. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 191 



PROBLEM NO. 6 

Nov. 15, 1919, A. M. D. R. Lat. 4° 15' N. Obs. Alt. Sun's L. L. 
50° 25'. Dip 30 ft. Chron. read 9h 33' 10" A. M., which was fast on 
Oct. 22d 3' 28" and losing 4".7 daily. Sun's compass bearing N 82° 30' E. 
Var. 25° E. Ship sailed from sight to noon N 79° E (true) 31 miles. Obs. 
Mer. Alt. Sun's L. L. 68° 13' S. 

Required course and distance from noon to 24° 18' N, 56° 28' W. 



Chron. 
Fast 


21h 33' 10" 

- 3' 28" 


4".7 rate 
23.9 days 


Ace. Rate 


21h 29' 42" 
+ 1' 52" 


112" = 1' 52" ace. rate 

Dec. 14d 20h 18° 15'.0 S 
Corr. 1.5h + I'.O 


G. M. T. 14d 

Eq. Time 


21h 31' 34" 
+ 15' 29" 


Dec. 14d 21. 5h 18° 16'.0 S 
P. D. = 108°16' 


G. A. T. 14d 

Obs. Alt. 
S.D. 


21h 47' 03" 

50° 25' 00" 
+ 16' 12" 



50° 41' 12' 



Dip 



R.&P. 



5' 22' 



50° 35' 50' 



41' 



Corr. Alt. 
Lat. 
P. D. 


50° 35' 09" 

4° 15' 00" 

108° 16' 00" 


Sec 
Csc 

Cos 
Sin 

True 

Obs. 
or 
E Erro 
Varif 

Devi 


.00120 
.02246 

9.16710 
9.71141 


Sec 
Sec 

Cos 
Cos 

54° 
125° 

82° 


.19728 
.00120 


s 

s-h 
s-P. D. 


2)163° 06' 09" 

81° 33' 04" 
30° 57' 55" 
26° 42' 56" 

21h 48' 42" 
21h 47' 03" 


9.16710 
9.95097 


L. A. T. 14d 
G. A. T. 14d 


8.90217 

Bearing S 

N 

Bearing N 

r 
ition 

ation 


9.31655 

10' E or 
50' E 
30' E 


Long, at Sight 


1' 39" 
0° 24' 45" 


43° 
25° 


20' E 
00' E 




18° 


E 



Course N 79° E, 31 miles. Diff. Lat. 5'9 miles = 5'.9. Departure 
30.4 miles. (Mid. Lat. 4°) = Diff. Long. 30'. 5 E. Long, at noon 0° 55' 
15" E or Oh 3' 41". 



192 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

G. A. T. 14d 23h 56' 19" Dec. 14d 22h 18° 16'.3 S 

Eq. Time - 15' 28" Corr. 1.7h 1'.2 



G. M. T. 14d 23h 40' 51" Dec. 14d 23'.7h 18' 17'.5 S 

Obs. Alt 68° 13' 00" 

S. D. + 16' 12" 

Dip 

R. &P. 

Corr. Alt. 
Z. D. 
Dec. 

Lat. at Noon 
Diff. Lat. 

Lat. at Sight 
Lat. Used 

Error 61'.9 N 

TABLE 47 

Lat. 3°. Bearing 55°. F = .70. Long. Corr. = .70x61'.9=43'.3 W. 
Long. 0° 24' 45" E 

Corr. 43' 18" W 



68° 


29' 
5' 


12" 

22" 




68° 


23' 


50" 
21" 




68° 
21° 

18° 


23' 
36' 
17' 


29" 
31" 
30" 


S 
N 
S 


3° 


19' 
5' 


01" 
54" 


N 
S 


3° 

4° 


13' 
15' 


07" 
00" 


N 
N 



Corr. Long, at Sight 0° 18' 33" W 

Diff. Long. 30' 30" E 



Corr. Long, at Noon ^ 0° 11' 57" E 

Lat. A 3° 19' N Mer. Part ' r97.8 Long. A 0° 12' E 

Lat. B 24° 18' N Mer. Part 1494.2 Long. B 56° 28' W 



Diff. Lat. 20° 59' or Mer. Part 1296.4 Diff. in Long. 56° 40' or 
1259' 3400' 

Log. of Diff. Long. 3400' =3.53148 
Log. of Mer. Part 1206' =3.11261 



Log. Tan. . 41887 = course 69° 08'. 

Log. Sec. 69* 08' = .44821 

Log. of Diff. Lat. 1259'= .10003 

Log. . 54834 = distance 3535 miles. 

At sight Lat. 3° 13' N, Long. 0° 18' 33" W 
At noon Lat. 3° 19' N, Long. 0° 11' 57" E 
Error 43° E. Dev. 18° E. 
Course N 69° 08' W. Dist. 3535 miles. 



CHAPTER XV 
LATITUDE BY MERIDIAN ALTITUDE OF PLANET 

This problem is worked the same as latitude by fixed 
star, with the exception that parallax must be applied to 
altitude, and the declination is to be corrected for Green- 
wich date and time. 

After finding Greenwich Mean Time, take out declina- 
tion of planet from almanac for Greenwich date, and the 
difference in small figures between it and next date. 

Note. — Notice whether declination is decreasing or 
increasing. 

Enter Table IV (Almanac) with the difference at top 
of page to the nearest number, and the G. M. T. on right- 
hand side to the nearest hour and minute, and read the 
number obtained from the column. 

Apply this number to Planet^s Declination for Green- 
wich date as follows: 

If decHnation is increasing, add the correction. 

If declination is decreasing, subtract the correction. 

Result will be true declination. 

Note. — If G. M. T. is over 12 hours, first find the number 
from Table IV that 12 hours will give, and then the balance 
of hours and minutes left, and add the two. 

For example: Jan. 24th G. M. T. 14h 14'. Required 
true declination of Planet ^' Venus." 

Planet's Dec. Jan. 24th = 16° 49'.0 S decreasing 
Corr. Table IV = - 13'.6 Diff. 230 



True Dec. = 16° 35^4 S or 16° 35' 24" S 

Looking in 230 column in Table IV, we find for 

12 hours 115 

For 2h 14' the balance, we find 21 



Adding the two = 136 Corr. 

193 



194 SIMPLE KULES AND PROBLEMS IN NAVIGATION 

As the declination is decreasing correction is to be sub- 
tracted. 

The Obs. Mer. Alt is corrected as follows: 

Index error as per sign, if any. 

Dip (Table 14) subtract. 

Parallax (Table 17) add. 

Refraction (Table 20 A) subtract. 

Result will be true altitude. 

Subtract true altitude from 90°, find zenith distance, and 
apply declination as in previous examples for latitude obser- 
vations. 

Result will be latitude. 



LATITUDE BY PLANET 



PROBLEM NO. 1 

Oct. 5, 1919. Obs. Mer. Alt. Planet Saturn 36° 15' 20" S. Dip 18 ft, 
Chron. read 3h 08' 04" P. M. Required latitude. 



G. M. T. 5d 

*Dec. 5d 
Corr. 3h 08' 


3h 08' 04" 

10° 26'.9 N 
0'.3 


decree 

N 
N 

N 


ising 


Dec. 5d 3h 08' 

Obs. Alt. 
Dip 


10° 
36° 


26'.6 N 

15' 20" 
4' 09" 


H. P. O'.Ol or 1" 


Par. (Table 17) 


36° 

+ 


11' 11" 
01" 




Ref. 


36° 


11' 12" 
1' 19" 




True Alt. 


36° 
90° 


09' 53" 
00' 00" 




Z.D. 
Dec. 


53° 
10° 


50' 07" 
26' 36" 




Lat. 


64° 


16' 43" 





SIMPLE RULES AND PROBLEMS IN NAVIGATION 195 

PROBLEM NO. 2 

Dec. 25, 1919. Obs. Mer. Alt. Planet Jupiter 41° 12' 00' N. Dip 
28 ft. Chron. read 6h 38' A. M. Required latitude. 
G. M. T. 24d 181i 38' 
*Dec. 24d 16° 18'.5 N increasing 

Corr. 18h 38' I'.l N 

H. P. O'.03or2'^ 



Dec. 24d 18h 38' 

Obs. Alt. 
Dip 


16° 19'.6 

41° 12' 00" 
5' 11" 


Par. (Table 17) 


41° 06' 49" 
+ 02" 


Ref. 


41° 06' 51" 
1' 07" 


True Alt. 


41° 05' 44" 
90° 00' 00" 


Z.D. 
Dec. 


48° 54' 16" S 
16° 19' 36" N 



Lat. 32° 34' 40" S 



PROBLEM NO. 3 



Jan. 2, 1919. Obs. Mer. Alt. Planet Venus 69° 07' 00" N. Dip 14 ft. 
Chron. read Ih 12' P. M. 



G. M. T. 2d 
Dec. 2d 
Corr. Ih 12' 


22° 


Ih 12' 
56'. 9 S decreasing 
0'.4 


Dec. 2d Ih 12' 

Obs. Alt 
Dip 


22° 
69° 


56'.5 S H. P. 0'.09 or 5' 

07' 00" N 
3' 40" 


Par. (Table 17) 


69° 


03' 20" 
05" 


R«f. 


69° 


03' 25" 
22" 


True Alt. 


69° 
90° 


03' 03" 
00' 00" 


Z.D. 
Dec. 


20° 
22° 


56' 57" S 
56' 30" S 


Ut. 


43" 


53' 27" S 



196 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 4 

Apr. 14, 1919. Obs. Mer. Alt. Planet Jupiter 68° 58' S. Dip'14 ft. 
Ghron. read Ih 40' P. M. 



G. M. T. 14d 


Ih 40' 


Dec. 14d 
Con. Ih 40' 


22° 23'. 1 N decreasing 
O'.O 


Dec. 14d Ih 40' 


22° 23'.1 N H. P. 0'.03 or 2' 


Obs. Alt. 
Dip 


68° 58' 00" 
- 3' 40" 



Par. 

Ref. 
True Alt. 



Z.D. 

Dec. 



68° 
■+ 


54' 


20" 

2" 




68° 


54' 


22" 
22" 




68° 
90° 


54' 
00' 


00" 
00" 




21° 
23° 


06' 
23' 


00" 
06" 


N 
N 



Lat. 44° 29' 06" N 



CHAPTER XVI 
LATITUDE BY EX-MERIDIAN ALTITUDE OF SUN 

This problem is to find the latitude of the place, when the 
sun is not visible at noon. 

It is possible at certain seasons of the year to obtain the 
latitude 28 minutes before or after noon. 

When sun's declination is opposite name to latitude of 
observer the interval is greater, when the latitude and 
declination are the same name the interval is less. 

If further away from noon than 28 minutes, the latitude 
may yet be calculated, but by a different method called 
0' 0" method. This method will be explained in another 
chapter. 

Find the Local Apparent Time (L. A. T.) as follows: 

Correct chronometer and obtain G. M. T. 

Take from the Nautical Almanac the equation of time 
for this G. M. T. and apply it, giving the G. A. T. 

Under G. A. T. put down longitude in time. If east 
longitude add; if west longitude, subtract; giving L. A. T. 

To find the time away from noon : 

If L. A. T. is less than 24 hours, subtract it from 24 hours 
and the result will be the minutes and seconds before noon. 
If L. A. T. is over hours it will be the mJnutes and seconds 
after noon. 

Take out sun's declination from almanac for Greenwich 
date and time. 

Square the number of minutes from noon. Using the 
nearest minute will be close enough for practical purposes. 

Note. — To square a number, multiply it by itself. For 
example: The square of 12' is 12 Xl2 = 144. 

Enter Table 26 (Bowditch) with latitude and declination 
to nearest degree, and read the number obtained from this 
table in its proper column. Declination will be found from 
top of page, latitude from side. 

Note. — Notice whether latitude and declination are same 
or contrary names. 

Multiply the square of minutes from noon by this num- 
ber, and the result will be seconds of altitude correction. 

Reduce the seconds to minutes and seconds, and always 
add it to sun's observed altitude. 

197 



198 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

Note. — Table 27 (Bowditch) is another method of find- 
ing the altitude correction. It is based on the same prin- 
ciple as the foregoing rule — that is, the square of the number 
of minutes from noon multiplied by correction from Table 26, 
is given in this table. 

After adding to observed altitude the correction, correct 
altitude for index error, semi-diameter, dip, refraction and 
parallax, and obtain true altitude. 

Find the zenith distance, and apply declination to same, 
as was done in meridian altitude sights. 

Result will be latitude at sight. 

To find the latitude at noon, it will be necessary to allow 
the difference of latitude made by the ship from the sight to 
noon on the course and distance steered in the interval. 

This problem is very useful to the navigator, for if the 
sun is overcast at noon the latitude by observation would be 
lost for that day, if this example was not used. 

PROBLEM NO. 1 

Mar. 10, 1919. Ex. Mer. Alt. Sun's L. L. 42° 16' 28" S. Dip 18 ft. 
Chron. read 6h 45' 15" P. M. Long. 94° 16' W. Lat. by D. R. 43° N. 

G. M. T. lOd 6h 45' 15" Dec. lOd 6h 4° 18'.4 S 

Eq. Time - 10' 34" Corr. for .7h - 0'.7 



G. A. T. 6h 34' 41" Dec. lOd 6.7h 4° 17'.7 S 

Long. 6h 17' 04" 



648" = 10'48"alt. corr. 



18 
L. A. T. Oh 17' 37" 18 

Time past noon 18' — 

324 
Obs. Alt. 42° 16' 28" 2" . from Table 26 

Alt. Corr. 

S.D. 

Dip 

R.&P. 
True Alt. 



Z.D. 
Dec. 



Lat. 43° 04' 01" N 



42° 

+ 


16' 
10' 


28" 
48" 


42° 

+ 


27' 
16' 


16" 
06" 


42° 


43' 

4' 


22" 
09" 


42° 


39' 


13" 
56" 


42° 
90° 


38' 
00' 


17" 
00" 


47° 
4° 


21' 
17' 


43" 

42" 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 199 



PROBLEM NO. 2 

Apr. 19, 1919. Ex. Mer. Alt. Sun's L. L. 41*' 28' 13" N. Dip 20 ft. 
Chron. read 4h 45' 08" A. M. Long. 105° 15' E. Lat. by D. R. 38° S. 

G. M. T. 18d 16h 45' 08" Dec. 18d 16h 10° 47'.1 N 

Eq. Time + 38" Corr. .7h + 0'.6 



G. A. T. 

Long. 


16h 45' 46" 
7h 01' 00" 


Dec. 18d 16'.7h 10° 47'.7 N 

13 
13 

169 

2".0 from Table 26 

338" =5' 38" alt. corr. 


L. A. T. 

Time before 

Obs. Alt. 
Alt. Corr. 


23h 46' 46" 
noon 13' 

41** 28' 13" N 
+ 5' 38" 


S.D. 


41° 
+ 


33' 51" 
16' 00" 


Dip 


41° 


49' 51" 
4' 23" 




R.&P. 


41° 


45' 28" 

58" 




True Alt. 


41° 
90° 


44' 30" 
00' 00" 


- 


Z.D. 
Dec. 


48° 
10° 


15' 30" S 

47' 42" N 





Lat. 37° 27' 48" S 



200 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 3 

Mar. 11, 1919. Ex. Mer. Alt. Sun's L. L. 45° 38' 25" N. Dip 22 ft. 
Chron. read Mar. 10, llh 59' 54", slow 35' 58". Long. 168° 20' E. 
D. R. Lat. 48° S. 



Chron. 
Slow 


lOd 
lOd 

efore 


llh 59' 
+ 35' 


54" 

58" 


Dec. lOd 12h 4" 12' 
Corr. for .6h - 0' 


.6S 
.6 


G. M. T. 

Eq. Time 


12h 35' 
10' 


52" 
30" 


Dec. lOd 12.6h 4° 12' 

21 
21 

441 

1".9 from Table 26 

838" = 13'58"alt. corr. 


S 


G. A. T. ; 

Long. 


12h 25' 
llh 13' 


22" 
20" 




L. A. T. 

Time b 

Obs. Alt. 
Alt. Corr. 


23h 38' 
noon 21' 

45° 38' 
+ 13' 


42" 

25" 

58" 




S.D. 


45° 
+ 


52' 
16' 


23" 

06" 




Dip 


46° 


08' 
4' 


29" 
36" 




R. &P. 


46° 


03' 


53" 
50" 




True Alt. 


46° 
90° 


03' 
00' 


03" 
00" 




Z.D. 
Dec. 


43° 
4° 


56' 
12' 


57" S 
00" s 




Lat. 


48° 


08' 


57" S 





SIMPLE RULES AND PROBLEMS IN NAVIGATION 201 



PROBLEM NO. 4 

July 4, 1919. Ex. Mer. Alt. Sun's L. L. 44° 02' N. Dip 18 ft. Chron. 
read lOh 17' 10" A. M., slow 3h 52' 17". Long. 35° 15' W. D. R. Lat. 
23° S. 



Chron. 
Slow 


22h 17' 
+ 3h 52' 

2h09' 
4' 


10" 
17" 

27" 
02" 


Dec. 4d 2h 22° 56'.9 N 
Corr. .Ih O'.O 


G. M. T. 4d 
Eq. Time 


Dec. 4d 2.1h 22° 56'.9 N 

16 
16 

256 

2".3 from Table 26 

589" = 9' 49" alt. corr. 


G. A. T. 

Long. 


2h05' 
2h21' 


25" 
00" 


L. A. T. 

Time before 

Obs. Alt 
Corr. 


23h44' 
noon 16'. 

44° 02' 
+ 9' 


25" 

00" N 
49" 


S.D. 


44° 11' 
+ 15' 


49" 
48" 




Dip 


44° 27' 
4' 


37" 
09" 




R.&P. 


44° 23' 


28" 
53" 






44° 22' 
90° 00' 


35" N 
00" 




Z.D. 
Dec. 


45° 37' 
22° 56' 


25" S 

54" N 




Lat. 


22° 40' 


31" S 





202 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 5 

Oct. 24, 1919. Ex. Mer. Alt. Sun's L. L. 37° 02' 15" S. Dip 18 ft. 
Chron. read 7h 07' 41" A. M., slow 16' 19". Long. 70° E. D. R. Lat. 
41° 13' N. 



Chron. 
Slow 


23d 
23d 

ast noo] 


19h 07' 

+ 16' 


41" 
19" 


Dec. 23d 18h 11° 23'.9 S 
Corr. 1.4h + 1'.3 


G. M. T. 

Eq. Time 


19h 24' 
+ 15' 


00" 
35" 


Dec. 23d 19.4h 11° 25'.2 S 

20 
20 

400 

1".8 from Table 26 

720" or 12' 00" alt. corr. 


G. A. T. : 

Long. 


19h 39' 
4h40' 


35" 


L. A. T. 

Timep 

Obs. Alt 
Corr. 


24h 19' 
a 20'. 

37° 02' 
+ 12' 


35" 

15" 
00" 


S.D 


37° 

4- 


14' 
16' 


15" 
06" 




Dip 


37° 


30' 
4' 


21" 
09" 




R. &P. 


37° 


26' 
1' 


12" 
09" 




True Alt. 


37° 
90° 


25' 
00' 


03" 
00" 




Z. D. 
Dec. 


52° 
11° 


34' 

25' 


57" N 
12" S 




Lat 


41° 


09' 


45" N 





SIMPLE RULES AND PROBLEMS IN NAVIGATION 203 



PROBLEM NO. 6 

Sept. 24, 1919. Ex. Mer. Alt. Sun's L. L. 50° 19' S. Dip 16 ft. 
Chron. read Oh 34' 10" P. M. fast 19' 20". Long. 6° W. D. R. Lat. 
38° 50' N. 



Chron. 

Fast 


Oh 34' 
19' 


10" 
20" 


Dec. 24d Oh 0° 9'.2 S 
Corr. .2h + 0'.2 


G. M. T. 24d 

Eq. Time 


Oh 14' 

+ 7' 


50" 
40" 


Dec. 24d 0.2h 0° 9'.4 S 

1.5 
1.5 

2.2 

2".4 from Table 26 

5.3" alt. corr. 


G. A. T. 24d 

Long. 


Oh 22' 
24' 


30" 
00" 


L. A. T. 23d 

Time before 

Obs. Alt. 
Corr. 


23h 58' 
noon r.5. 

50° 19' 
+ 


30" 

00" S 
05" 


S.D. 


50° 19' 
+ 16' 


05" 
00" 




Dip 


50° 35' 
3' 


05" 
55" 




R. &P. 


50° 31' 


10" 

42" 




True Alt. 


50° 30' 
90° 00' 


28" S 
00" 




Z.D. 
Dec. 


39° 29' 
0° 09' 


32" N 
24" S 




Lat. 


39° 20' 


08" N 





204 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 7 

Dec. 25, 1919. Ex. Mer. Alt. Sun's L. L. 64° 45' N. Dip 15 ft. 
Chron. read 3h 17' 10" A. M., slow 13' 05". Long. 130° E. D. R. Lat. 

48° 23' S. 

Chron. 15h 17' 10" Dec. 24d 14h 23° 25'.7 S 

Slow + 13' 05" Corr. 1.5h - O'.l 



G. M. T. 24d 15h 30' 15" Dec. 24d 15.5h 23° 25'.6 S 

Eq. Time + 24" 



G. A. T. 24d 15h 30' 39" 11 

Long. + 8h 40' 00" 



L. A. T. 24d 241i 10' 39" 

Time past noon of 25th day, 10' 
39". 

Obs. Alt. 64° 45' 00" N 

Corr. + 5' 51" 



S. D. 
Dip 

R. &P. 

True Alt. 



11 
11 

121'x2".9=351"or5'51' 



Z. D. 
Dec. 



Lat 48° 22' 38" S 



64° 

+ 


50' 
16' 


51" 

18" 




65° 


07' 
3' 


09" 

48" 




65° 


03' 


21" 
23" 




65° 
90° 


02' 
00' 


58" 
00" 


N 


24° 
23° 


57' 
25' 


02" 
36" 


S 

s 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 205 



PROBLEM NO. 8 

May 29, 1919. Ex. Mer. Alt. Sun's L. L. 64° 25' S. Dip 10 ft. 
Chron. read llh 17' 56" A. M., slow 3h 53'. Long. 49° 30' W. D. R 
Lat. 47° N. 



Chron. 
Slow^ 


23h 17' 56" 
3h 53' 00" 


Dec. 29d 2h 21° 30'.6 N 
Corr. 1.2h + 0'.5 


G. M. T. 29d 
Eq. Time 


3h 10' 56" 

+ 2' 54" 


Dec. 29d3.2h 21° 31'.1 N 

4 
4 

16 
2".9 from Table 26 

46" alt. corr. 


G. A. T. 29d 

Long. 


3h 13' 50" 
3h 18' 00" 


L. A. T. 28d 

Time before 

Obs. Alt. 
Corr. 


23h 55' 50" 
noon 4' 10". 

64° 25' 00' S 
+ 46" 


S.D. 


64° 25' 46" 
H- 15' 48" 




Dip 


64° 41' 34" 
( -- 3' 06" 




R.&P. 


64° 38' 28" 
- 23" 




True Alt. 


64° 38' 05" S 
90° 00' 00" 




Z. D. 
Dec. 


25° 21' 55" N 
21° 31' 06" N 




Lat. 


46° 53' 01" N 





206 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 9 

Jan. 24, 1919. Ex. Mer. Alt. Sun's L. L. 22° 46' S. Index error 
-1' 25". Dip 26 ft. Chron. read lOh 5' 2" P. M., which was slow 7' 
15". Long. 155° W. D. R. Lat. 48° N. 



Chron. 
Slow 


lOh 05' 02" 

+ 7' 15" 


Dec. 
Corr 

Dec. 


24d lOh 19^ 17'.4 S ^ 
. .2h - O'.l 


G. M. T. 24d 

Eq. Time 


lOh 12' 17" 
- 12' 09" 


24d 10.2h 19° 17'.3 S 

20 
20 

400 

r.4 from Table 26 

560" = 9'20"alt. corr. 


G. A. T. 24d 
Long. 


lOh 00' 08" 
-10h20' 00" 


L. A. T. 23d 
Time before 

Obs. Alt. 
Corr. 


23h 40' 08" 
noon 19' 52". 

22° 46' 00" S 
4- 9' 20" 


LE. 


22° 55' 20" 
1' 25" 




S.D. 


22° 53' 55" 
+ 16' 18" 




Dip 


23° 10' 07" 
- 5' 00" 




R.&P. 


23° 05' 07" 
2' 07" 




True Alt. 


23° 03' 00" S 
90° 00' 00" 




Z.D. 
Dec. 


66° 57' 00" N 
19° 17' 18" S 




Lat. 


47° 39' 42" N 





SIMPLE RULES AND PROBLEMS IN NAVIGATION 207 



PROBLEM NO. 10 

July 12, 1919. Ex. Mer. Alt. Sun's L. L. 78° 16' 30" S. Dip 26 ft. 
Chron. read 5h 0' 28" P. M. Long. 75° 18' W. D. R. Lat. 34° N. 



G. M. T. 12d 
Eq. Time 


5h 00' 28" 
5' 19" 


Dec. 
Corr, 

Dec. 


12d4h 
. l.Oh 

12d5h 

6 
6 

36 
r'.3froi 

263" = 4' 


22° 04'.1 N 
0'.3 


G. A. T. 12d 

Long. 


4h 55' 09" 
- 5h 01' 12" 


22° 03'.8 N 


L. A. T. lid 
Time before 

Obs. Alt. 
Corr. 


23h 53' 57" 
noon 6' 03" 

78° 16' 30" S 
+ 4' 23" S 


n Table 26 
23" alt. corr. 


S.D. 


78° 20' 53" 
4- 15' 45" 


Dip 


78° 36' 38" 
5' 00" 




R.&P. 


78° 31' 38" 
- 9" 




True Alt. 


78° 31' 29" S 
90° 00' 00" 




Z.D. 
Dec. 


11° 28' 31" N 
22° 03' 48" N 




Lat. 


33° 32' 19" N 





208 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 11 

Sept. 18, 1919. Ex. Mer. Alt. Sun's L. L. 78° 16' 30" S. Dip 26 ft. 
Chron. read 7h 03' 00" A. M. Long. 75° 30' E. D. R. Lat. 13° N. 

G. M. T. 17d 19h 03' 00" Dec. 17d 18h 2° 16'.6 N 

Eq. Time + 5' 29" Corr. l.Oh - I'.O 

G. A. T. 17d 19h 08' 29" Dec. 17d 19h 2° 15'.6 N 
Long. + 5h 02' 00" 



10 



L. A. T. 17d 24h 10' 29" 10 

Time after noon 10' 29" — 

100 
Obs. Alt. 78° 16' 30" S 10" from Table 26 
Con. + 16' 40" 



1000"=16'40"alt. corr 



78° 33' 10' 
S. D. -f 16' 00' 



78° 49' 10' 
Dip - 5' 00' 



78° 44' 10' 



R. &P. 


9" 


True Alt. 


78° 44' 01" S 
90° 00' 00" 


Z. D. 
Dec. 


11° 15' 59" N 
2° 15' 36" N 


Lat. 


13° 31' 35" N 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 209 



PROBLEM NO. 12 

Feb. 7, 1919. Ex. Mer. Alt. Sun's L. L. 42° 00' 30" S. Dip 18 ft. 
Chron. read 6h 45' 15" P. M. Long. 94° W. D. R. Lat. 33° N. 



G. M. T. 

Eq. Time 


7d 
7d 

ter 


6h45' 
14' 


■ 15" 
' 16" 


Dec. 7d 6h 15° 27'.9 S 
Corr. .8h - 0'.6 


G. A. T. 

Long. 


61i30' 
- 6h 16' 


59" 
00" 


Dec. 7d 6.8h 15° 27'.3 S 

15 
15 

225 

2".l from Table 26 

472" 7' 52" alt. corr. 


L.A.T.7d 
Time af 

Obs. Alt. 
Corr. 


Oh 14' 
noon 14' 59' 

42° 00' 

+ 7' 


59" 

7 

30" S 
52" 


S.D. 


42° 08' 
+ 16' 


22" 
12" 


Dip 


42° 24' 
4' 


34" 
09" 




R. &P. 


42° 20' 


25" 

57" 




True Alt. 


42° 19' 
90° 00' 


28" S 
00" 




Z. D. 

Dec. 


47° 40' 
15° 27' 


32" N 
18" S 




Lat. 


32° 13' 


14" N 





210 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 13 

June 23, 1919. Ex. Mer. Alt. Sun's L. L. 41* 20' 30" N. Dip 20 ft 
Chron. read 4h 40' 18" A. M. Long. 104° 50' E. D. R. Lat. 25° S. 



G. M. T. 22d 
Eq. Time 


16h 40' 18" 
- 1' 42" 


Dec. 22d 16h 23° 26'.8 N 
Corr. .7h O'.O 


G. A. T. 22d 
Long. 


16h 38' 36" 
6h 59' 20" 


Dec. 23° 26'.8 N 

22 
22 

484 

2".2 from Table 26 

1065" = 17'45"alt. corro 


L. A. T. 23d 

Time before 

Obs. Alt. 
Corr. 

S.D. 

Dip 


23h 37' 56" 
noon 22' 04". 

41° 20' 30" N 
+ 17' 45" 

41° 38' 15" 
-h 15' 48" 

41° 54' 03" 
- 4' 23" 


R.&P. 


41° 


49' 40" 
58" 




True Alt. 


41° 
90° 


48' 42" 
00' 00" 




Z. D. 
Dec. 


48° 
23° 


11' 18" S 

26' 48" N 




Lat 


24° 


44' 40" S 





SIMPLE RULES AND PROBLEMS IN NAVIGATION 211 



PROBLEM NO. 14 

Mar. 14, 1919. Ex. Mer. Alt. Sun's L. L. 45'' 30' 50" N. Index 
error -V 50". Dip 21 ft. Chron. read Oh 50' 45" A. M., slow 25' 50". 
Long. 167° 50' E. D. R. Lat. 47° S. 

Chron. 12h 50' 45" Dee. 13d 12h 3*^ 01'.9 S 

Slow + 25' 50" Corr. 1.8h -- 1'.3 



G. M. T. 13d 13h 16' 35" Dec. 13d 13.8h 3° 00'.6 S 

Eq. Time - 9' 42" 



G. A. T. 13d 13h 06' 53" 18 

Long. llh 11' 20" 

L. A. T. 14d Oh 18' 13" 1''.9 from Table 26 

Time after noon 18' 13" 

Obs. Alt. 45° 30' 50" N 

Corr. + 10' 15" 



18 
18 

324 

615" =10' 15" alt. Gorr. 



45° 41' 05" 
I. E. - 1' 50" 



45° 39' 15" 
S. D. H- 16' 06" 



45° 55' 21" 
Dip - 4' 29'^ 



45° 50' 52" 



R. & P. 


50" 


True Alt. 


45° 50' 02" N 
90° 00' 00" 


Z.D. 
Dec. 


44° 09' 58" S 
3° 00' 36" S 


Lat. 


47** 10' 34" S 



CHAPTER XVII 
LONGITUDE BY FIXED STAR AND PLANET 

This problem is to determine the longitude of a place bj^ a 
jBxed star and planet, and is accura^te as long as the horizon 
is clear enough to obtain the proper altitude. 

A star in the East and another in the West taken as 
close as possible to each other, and projected on the chart 
by Sumner lines, will make an excellent '' fix " for the ship. 

For fixed stars: 

Correct chronometer same as was done in longitude by 
sun observations, and obtain Greenwich Mean Time. 

From Page 2 (Almanac) take out Sun's Right Ascension 
for Greenwich date, and place it under G. M. T. 

From table below on Page 2 take out correction to be 
added to Sun's Right Ascension, using G. M. T. 

Add together G. M. T., Sun's Right Ascension and 
Correction. Result will be Greenwich Siderial Time, ex- 
pressed G. S. T. 

Take out star's declination from Page 95 (Almanac) for 
month of example, and star's right ascension from opposite 
page for month. 

Find polar distance as follows: 

Latitude and declination same name, subtract declina- 
tion from 90°. 

Latitude and declination different name, add 90° to 
declination. 

Correct star's observed altitude as follows: 

Index error as per sign, if any. 

Dip (Table 14) subtract. 

Refraction (Table 20 A) subtract. 

Result will be true altitude. 

Add together true altitude, latitude and polar distance, 
and divide sum by 2. Result will be half sum. 

Subtract true altitude from half sum. Result will be 
remainder. 

212 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 213 

From Table 44 (Bowditch) take out the following 
logarithms : 

Secant of latitude. Rejecting 10 from index number. 

Cosecant of polar distance. Rejecting 10 from index 
munber. 

Cosine of half sum. 

Sine of remainder. 

Note. — If polar distance exceeds 90°. Take secant of 
declination instead. 

Add these four logarithms together, and subtract 10 
from index number. 

Log. Haversine (Table 45) that agrees with sum of log- 
arithms will be star's hour angle. Always to be read from 
top of page or in P. M. 

Under star's right ascension put down star's hour angle 
and apply as follows : 

If star bore West when observation was taken, add the two. 

If star bore East when observation was taken, subtract 
star's hour angle from star's right ascension. Result will 
be siderial time ship, expressed S. T. S. 

Note. — If star bore East, and hour angle is greater than 
right ascension, add 24 hours to right ascension before 
making subtraction. 

Under siderial time at ship, put down Greenwich Siderial 
time, and subtract less from greater. Result will be longi- 
tude in time. 

Turn longitude in time into degrees, minutes and seconds 
as in previous methods. Result will be longitude. 

If Greenwich time is best the longitude is West. 

If Greenwich time is least the longitude is East. 



214 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 1 

Jan. 31, 1919, A. M. Obs. Alt. *Spica 45* 50', bearing W. Dip 
36 ft. Chron. read Ih 14' 35" P. M., which was fast Jan. 11, 31' 34" and 
gaining 9" daily. Lat. 25° 53' N. D. R. Long. 94° W. 



Chron. 
Fast 


Ih 14' 35" 
- 31' 34" 


Dec. 
P.D. 

00" 
53" 


Interval 
Rate 


20 days 
9" 


Ace. Rate 


Oh 43' 01" 
3' 00" 


180" = 3' 

10° 44'.5 S 
90° OO'.O 


G. M. T. 31d 
R. A. M. S. 
Corr. 


Oh 40' 01" 
20h 38' 38" 

7" 


100* 44'.5 


G. S. T. 

Obs. Alt. 
Dip. 


21h 18' 46" 

45° 50' 
5' 





45° 


44' 


07" 


— 




57" 


45° 


43' 


10" 


25° 


53' 


00" 


100° 


44' 


30" 


J)172° 


20' 


40" 



Ref. 

h 

Lat. 25° 53' 00" Sec .04591 

P. D. 100° 44' 30" Csc .00768 



I 86° 10' 20" Cos 8.82451 

i-h 40* 27' 10" Sin 9.81212 



Log. Hav. 8.69022 



*R. A. 13h 20' 57' 

*H. A. Ih 42' 19' 



L. S. T. 15h 03' 16' 

G. S. T. 21h 18' 46' 



Long. ah 15' 30" -93* 52' 30" W 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 215 



PROBLEM NO. 2 

Jan. 30, 1919, A. M. Obs. Alt. *Vega 43° 57', bearing E. Dip 36 ft. 
Chron. read Oh 56' 00" P. M., fast 34' 25". Lat. 28° 27' N. Long, by 
D. R. 90° 30' W. 



Chron. 
Fast 


Oh 56' 00" 
34' 25" 


Dec. 
P.D. 

00" 
53" 


38° 42' 
90° 00' 


18" N 
00" 


G. M. T. 30d 
R. A. M. S. 

Corr. 


Oh 21' 35" 

20h 34' 41" 

03" 


51° 17' 


42" 


G. S. T. 30d 

Obs. Alt. 
Dip 


20h 56' 19" 

43° 57' 
5' 





43° 


51' 
1' 


07" 
01" 


43° 

28° 
61° 


50' 
27' 
17' 


06" 
00" 
42" 


2)123° 


34' 


48" 



Ref. 

h 

Lat. 28° 27' 00" Sec .05590 

P.D. 61° 17' 42" Csc .10784 



s 61° 47' 24" Cos 9.67459 

s-h 17° 57' 18" Sin 9.48893 



Log. Hav. 9.32726 



*R. A. 18h 34' 11" 

*H. A. 3h 39' 34" E or— 



L. S. T. 14h 54' 37" 

G. S. T. 20h 56' 19" 



Long. 6h or 42" or 90° 25' 30" W. 



216 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 3 

June 12, 1919, P. M. Obs. Alt. *Regulus 26° 18' 32", bearing West. 
Dip 17 ft. Chron. read 2h 02' 12" P. M., fast 14' 8". Lat. 37° 18' N. 
Long, by D. R. 110° E. 

12° 21'.6 N 
90° OO'.O 



Chron. 
Fast. 


S. 


2h 02' 12" 
14' 08" 


18' 
4' 


Dec. 


G. M. T. 
R. A. M. 

Corr. 


Ih 48' 04" 
5h 19' 03" 

18" 


P.D. 


G. S. T. 

Obs. Alt. 
Dip 


7h 07' 2b" 

26° 


32" 

02" 



26° 


14' 
1' 


30" 

58" 


26° 
37° 

77° 


12' 
18' 

38' 


32" 
00" 
24" 


2)141° 


08' 


56" 



*R. A. lOh 04' 05' 

*H. A. 4h 25' 20' 



L. S. T. 14h 29' 25' 

G. S. T. 7h 07' 25' 



77° 38'.4 



Ref. 

h 

Lat. 37° 18' 00" Sec .09937 

P. D. 77° 38' 24" Csc .01019 



s 70° 34' 28" Cos 9.52190 

s-h 44° 21' 56" Sin 9.84462 



Log. Hav. 9.47608 



Long. 7h 22' 00" or 110° 30' 00" E. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 217 



PROBLEM NO. 4 

Mar. 11, 1919, A. M. Obs. Alt. *Antares 28° 16' 15", bearing W. 
Dip 21 ft. Chron. read 8h 16' 23" P. M., slow 32' 18". Lat. 22° 18' S. 
Long, by D. R. 166° 10' W. 



Chron. 
Slow 


8h 16' 23" 
-h 32' 18" 


Dec. 
P.D. 

15" 
29" 


26° 15'.2 S 
90° OO'.O 


G. M. T. 
R. A. M. S. 

Corr. 


8h 48' 41" 

23h 12' 23" 

1' 27" 


63° 44'.8 


G. S. T. 

Obs. Alt. 
Dip 


32h 02' 31" 

28° 16' 
4' 





28° 11' 46' 
Ref. - 1' 48' 



h 

Lat. 
P.D. 




28° 09' 
22° 18' 
63° 44' 

2)114° 12' 


58" 
00" 

48" 

46" 


Sec 
Csc 


s 
s-h 




57° 06' 
28° 56' 


23" 
25" 


Cos 
Sin 

Log. Hav. 




*R.A. 
*H.A. 

L. S. T. 
G. S. T. 

Long, 


16h 24' 
4h33' 


28" 
59" 






20h 58' 
32h 02' 


27" 
31" 






llh 04' 


04" 


or 166° or 00' 



.03376 
.04728 



9.73486 
9.68476 

9.50066 



W 



218 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 5 

Dec. 16, 1919, P. M. Obs. Alt. *CapelIa 31° 17' 12", bearing E. 
Dip 19 ft. Chron. read lOh 12' 16" P. M., slow 8' 03". Lat. 6° 48' N. 
Long, by D. R. 33° 15' W. 



Chron. 
Slow 


lOh 12' 16" 
+ 8' 03" 


Dec. 
P.D. 

12" 
16" 


45° 55' 
90° 00' 


G. M. T. 
R. A. M. S. 
Corr. 


lOh 20' 19" 

17h 36' 19" 

1' 42" 


44° OS' 


G. S. T. 

Obs. Alt. 
Dip 


27h 58' 20" 

31° 17' 
4' 





31° 


12' 


56" 




1' 


36" 



Ref. 

h 31° 11' 20" 

Lat. 6° 48' 00" Sec .00307 

P.D. 44° 05' 00" Csc .15758 



9 87754 
s-h 9° 50' 50" Sin 9! 23305 





6° 48' 00" 
44° 05' 00" 


Sec 
Csc 




2)82° 04' 20" 






41° 02' 10" 
9° 50' 50" 


Cos 
Sin 

Log. 


*R.A. 
*H. A. 


5h 10' 50" 

3h 24' 50" 




L. S. T. 
G. S. T. 


Ih 46' 00" 
3h 58' 20" 





9.27124 



Long. 2h 12' 20" or 33° 05' 00" W 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 219 



PROBLEM NO. 6 

Apr. 16, 1919, P. M. Obs. Alt. *Aldebaran 23° 13' 20", bearing W. 
Dip 26 ft. Chron. read 7h 01' 35" P. M., fast 2' 27". Index error 
-2' 00'. Lat. 11° 47' S. Long, by D. R. 0° 05' E. 



Chron. 
Fast 


S. 

♦R.A. 
*H.A. 

L. S. T. 
G. S. T. 


7h 01' 35" Dc 

2' 27" 


JC. 

D. 

Sec 
Csc 

Cos 

Sin 

Log. Hav. 


16° 
90° 


20'.8 
OO'.O 


G. M. T. 
R. A. M. ; 

Corr. 


6h 59' 08" P. 
lb 34' 19" 
1' 09" 


106° 


20',8 


G. S. T. 

Obs. Alt. 
LE. 


8h 34' 36" 

23° 13' 20" 
2' 00" 




Dip 


23° 11' 20" 
5' 00" 




Ref. 


23° 06' 20" 
- 2' 15" 




h 

Lat. 

P.D. 


23° 04' 05" 

11° 47' 00" 

106° 20' 48" 


.00925 
.01792 


s 


2)141° 11' 53" 

70° 35' 56" 
47° 31' 51" 

4h 31' 17" 
4h 05' 42" 


9.52138 

9.86785 




9.41640 




8h 36' 59" 
8h 34' 36" 





Long. 2' 23" or 0° 35' 46" E 



220 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 7 

Dec. 1, 1919, P. M. Obs. Alt. *Capella 31° 17' 12", bearing E. Dip 
19 ft. Chron. read 9h 18' 16" P. M., slow 8' 03". Lat. 6° 48" N. Long, 
by D. R. 5° W. 

Chron. 9h 18' 16" Dec. 45° 55' 

Slow -4- 8' 03" 90° 00' 



9h 18' 16" 
8' 03" 


Dec. 


9h 26' 19" 

16h 37' 10" 

1' 33" 


P.D. 


26h 05' 02" 

31° 17' 
- 4' 


12" 
16" 



31° 


12' 
1' 


56" 
36" 


31° 

6° 

44° 


11' 
48' 
05' 


20" 
00" 
00" 


2)82° 


04' 


20" 





41° 02' 10" 
9° 50' 50" 


Cos 
Sin 

T iCicr 


*R.A. 
*H. A. 


5h 10' 49" 
3h 24' 50" 




L. S. T. 
G. S. T. 


Ih 45' 59" 
2h 05' 02" 





G. M. T. 9h 26' 19" P. D. 44° 05' 

R.A.M.S. 

Corr 

G. S. T. 

Obs. Alt. 
Dip 



Rfif. 

h 

Lat. 6° 48' 00" Sec .00307 

P.D. 44° 05' 00" Csc .15758 



9.87754 
s-h 9° 50' 50" Sin 9.23307 



9.27126 



Long. 19' 03" or 4^ 45' 45" W 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 221 



PROBLEM NO. 8 

Feb. 15, 1919, A. M. Obs. Alt. *Spica 48° 10', bearing W. Dip 26 ft. 
Chron. read Ih 14' 35", P. M., which was fast on Jan. 11, 31' 34", and 
gaining 9" daHy. Lat. 25° 53' N. Long, by D. R. 112° 45' W. 



Chron. 
Fast 


Ih 14' 35" 
- 31' 34" 


00" 
00" 


Interval 
Rate 

Dec. 
P. D. 


35 days 
9" daily 


Ace. Rate 


Oh 43' 01" 
- 5' 15" 


315" = 5' 15' 

10° 44'.5 S 
90° OO'.O 


G. M. T. 
R. A. M. S. 
Corr. 


Oh 37' 46" 

21'h 37' 46" 

06" 


100° 44'.5 


G. S. T. 

Obs. Alt. 
Dip 


22h 15' 38" 

48° 10' 
5' 





48° 


05' 
0' 


00" 

47" 


48° 

25° 

100° 


04' 
53' 
44' 


13" 
00" 
30" 


2)174° 


41' 


43" 



Ref. 

h 

Lat. 25° 53' 00" Sec .04591 

P. D. 100° 44' 30" Csc .00768 



s 87° 20' 52" Cos 8. 66! 35 

s-h 39° 16' 39" Sin 9.8014(3 



Log. Hav. 8.52040 



*R. A. 13h 20' 58" 

*H. A. Ih 23' 55" 



L. S. T. 14h 44' 53' 

G. S. T. 22h 15' 38' 



Long. 7h 30' 45" or 112^ 41' 15" W 



222 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 9 

Mar. 20, 1918, P. M. Obs. Alt. *Betelgeux 32° 17' 30", bearing E. 
Dip 26 ft. Chron. read 13h 16' 23", fast 3' 46". Lat. 32° 17' N. Long. 
by D. R. 164° 30' W. 



Chron 
Fast 


13h 16' 23" 
3' 46" 


30" 
00" 


Dec. 
P.D. 


7° 23'.4N 
90° OO'.O 


G. M. T. 

R. A. M. S. 
Corr. 


13h 12' 37" 

23h 47' 52" 
2' 10" 


82° 36'.6 


G. S. T. 

Obs. Alt. 
Dip 


37h 02' 39" 

32° 17' 

- 5' 





32° 


12' 

r 


30" 

28" 


32° 
32° 

82° 


11' 

17' 
36' 


02" 
00" 

36" 


2)147° 


04' 


38" 



Ref. 

h 

Lat. 32° 17' 00" Sec .07293 

P. D; 82° 36' 36" Csc .00362 

2 )147° 04' 38" " 

s 73° 32' 19" Cos 9.45235 

s-h" 41° 21' 17" Sin 9.82002 



•R. A. 5h 50' 49" 

*H. A. 3h 45' 36" 



L. S. T. 2h 05' 13' 

G. S. T. 13h 02' 39' 



Log. Hav. 9.34892 



Long. lOh 57' 20" or 164° 21' 30" W 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 223 



PROBLEM NO. 10 

Feb. 16, 1919, P. M. Obs. Alt. *Rigel 24° 18', bearing W. Index 
error +2' 12". Dip 24 ft. Chron. read llh 16' 28" P. M., which was 
fast on Jan. 10, 14' 12" and gaining 2".8 daily. Lat. 16° 46' N. Long, 
by D. R. 7° 45' E. 

Chron. llh 16' 28" Interval 37.5 days 

Fast - 14' 12" 2".8 rate 



105" = !' 45" 
Ace. Rate 

Dec. 8° 17'.8 S 

G. M. T. llh 00' 31" 90° OO'.O 



llh 16' 28" 
14' 12" 




llh 02' 16" 
1' 45" 




llh 00' 31" 

21h 41' 43" 

1' 48" 




32h 44' 02" 

24° 18' 
+ 2' 


00" 
12" 


24° 20' 

- 4' 


12" 
48" 


24° 15' 

- 2' 


24" 
09" 


24° 13' 
16° 46' 
98° 17' 


15" 
00" 

48" 


2)139° 17' 


03" 



R. A. M. S, 

Corr. 1' 48" P. D. 98° 17'.8 

G. S. T. 

Obs. Alt. 
LE. 



Dip 



Ref. 

h 

Lat. 16° 46' 00" Sec ,01887 

P. D. 98° 17' 48" Csc .00457 



s 69° 38' 31" Cos 9.54144 

s-h 45° 25' 17" Sin 9.85262 



*R. A. 5h 10' 41" 

*H. A. 4h 06' 03" 



Log. Hav.'- 9.41750 



*L. S. T. 9h 16' 44" 

G. S. T. 8h 44' 02" 



Long, 32' 42" or S" 10' 30" E 



LONGITUDE BY PLANET 

This problem is worked in the same manner as longitude 
by fixed star, with the exception that the planet's declina- 
tion and right ascension must be corrected for the Green- 
wich date and time. 



224 SIMPLE RULES AND PROBLEMS IX NAVIGATION 

After finding G. M. T. take out planet's declination and 
right ascension for Greenwich date, and correct it from 
Table IV (Almanac) same as was done in latitude by planet. 

Correct the altitude for index error, dip, parallax and 
refraction. 

After making these corrections the balance of the prob- 
lem will be worked in the same manner as longitude by fixed 
star. 



PROBLEM NO. 1 

Jan. 31, 1919, A. M. Obs. Alt. Planet Mars 18° 55', bearing E. 
Dip 36 ft. Chron. read Ih 11' 13" P. M., fast 34' 34". Lat. 25° 53' N. 
Required longitude? 



Parallax 



Ref. 



Chron. 
Fast 


Ih 11' 13" 
34' 34" 


00 
53 


*Dec. 

Corr. Table IV- 

For 36' 

P. D 

n 


11° 16' S 
-N. A. 

0' 


G.M.T.31d 
R. A. M. S. 

Corr. 


Oh 36' 39" 

20h 38' 38" 

6" 


Decl. 11° 16' 
90° 00' 


G. S. T. 

Obs. Alt. 
Dip 


21h 15' 23" 

18° 55' 
- 5' 


101° 16' 



18° 49' 07' 
+ 04' 

18° 49' 11' 



2' 49' 



h 

Lat. 

P.D. 


able IV) 
A. 


18° 46' 

25° 53' 

101° 16' 


22" 

00 

00" 


Sec 
Csc 

Cos 

Sm 

Log. Hav. 
Eor- 


.04591 
.00845 


8 


2)145° 55' 

72° 57' 
54° 11' 

22h 21' 


22" 

41" 
19" 

54" 
0" 


9.46689 

9.90S99 


*R.A. 

Corr. (T 


9.43024 


Con. R. 
H.A. 


22h 21' 
4h 10' 


54" 
05" 




L. S. T. 
G. S. T. 


18h 11' 
21h 15' 


49" 
23" 





Long. 



3h 03' 34" or 45° 53' 30" W 



mMPLE RULES AND PROBLEMS IN NAVIGATION 225 



PROBLEM NO. 2 

July 6, 1919, A. M. Obs. Alt. Planet Saturn 30° 16' 28", bearing E. 
Dip 16 ft. Chron. read 4h 16' 28", P. M., fast 3' 28". Lat. 27° 18' N. 

Chron. 4h 16' 28" *Dec. 6d 14° 16'.6 N 

Fast 3' 28" Corr. 4.2h (Table IV) 0'.4 



G. M. T. 4h 13' 00" Dec. 6d 4.2h 14° 16'.2 N 

R. A. M. S. 6h 53' 40" 90° OO'.O 

Corr. 41" 



G. S. T. llh 07' 2r 



30° 


12' 


33" 
0" 


30° 


12' 
1' 


33" 
40" 


30° 

27° 

75° 


10' 

18' 
43' 


53" 
00" 

48" 


2)133° 


12' 


41" 



*R. A. 9h 53' 36' 

Corr. (Table IV— N. A.) + 4" 



Corr. R. A. 9h 53' 40" 

H. A. 4h 12' 23" E or- 



L. S. T. 5h 41' 17' 

G. S. T. llh 07' 21' 



P. D. 75° 43'.8 



Obs. Alt. 30° 16' 28" 

Dip ~ 3' 55" 



Par. 



Ref. 

h 

Lat. 27° 18' 00" Sec 0.05129 

P.D. 75° 43' 48" Csc 0.01361 



66° 36' 20" Cos 9.59885 

36° 25' 27" Sin 9.77361 



Log. Hav. 9.43736 



Long. 6h 26' 04" or 81° 31' 00" W 



CHAPTER XVIII 
LATITUDE BY MERIDIAN ALTITUDE OF MOON 

This problem is useful to find the latitude when the moon 
is on the meridian in daylight, but at night cannot be 
depended upon on account of the sea horizon not being clear 
enough for proper altitude. 

The time of the Moon's Meridian Passage for Greenwich 
is given on Pages 76-77 (Nautical Almanac) and the differ- 
ence between transit in small figures. By entering Table IV 
(Almanac) with difference of transit at top of page, and 
longitude in time at right-hand side, will give the correction 
to be applied to Greenwich transit, to find the time of Moon's 
Meridian Passage at ship. 

In west longitude it is to be applied forward. 

In east longitude it is to be applied backward. 

Correct the chronometer and find the Greenwich date and 
time. 

The Moon's declination changes very fast, and the Nau- 
tical Almanac gives the declination for every 2 hours of the 
day, and the difference in small figures between the even 
hours. 

Take out declination for Greenwich date and closest hour, 
and the difference in small figures. 

Enter Table IV (Almanac) with difference at top of page, 
and number of minutes past the hour in the left-hand column, 
and read the correction for declination in its proper coliunn. 

Apply this correction to declination as follows: 

Declination decreasing, subtract. 

Declination increasing, add. 

Result will be true declination. 

Take out the Moon's S. D. (Semi-Diameter) and H. P. 
(Horizontal Parallax) from almanac opposite the hour used. 

Put down the observed meridian altitude and apply the 
S. D. Add for Lower, and subtract for Upper Limb. 

Subtract the Dip (Table 14). 

226 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 227 

Enter Table 24 (Bowditch) with H. P. at top of page, and 
apparent altitude at side, and read correction in proper 
column. 

This correction will be the Parallax and Refraction, 
always to be added to Altitude. 

This will give the true altitude. 

Subtract true altitude from 90°, find zenith distance, and 
apply declination as in previous examples for latitude. 

Result will be latitude. 



LATITUDE BY MOON 



PROBLEM NO. 1 

Feb. 12, 1919. Obs. Mer. Alt. Moon's L. L. 28° 14' 00'' S. 
Dip 28 ft. Chronometer read 4h 16' 28" P. M. 

G. M. T. 12d 4h 16' 28" 

Dec. 12d 4h 17° 41 '.5 N decreasing 

Corr for 16'.5 2'.2 



Dec. 12d 4h 16'.5 17° 39'.3 N 

S. D. 15'.6 Horizontal parallax 57'.3 

Obs. Alt. 28° 14' 00" 

S. D. + 15' 36" 



28° 29' 36" 
Dip - 5' 11" 



28° 24' 25" 
Par. and Ref. (Table 24) + 49' 00" 



True Alt. 29° 13' 25" S 

90° 00' 00" 



Z. D. 60° 46' 35" N 

Dec. 17° 39' 18" N 



Lat. 78° 25' 53" N 



228 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 2 

Mar. 18, 1919. Obs. Mer. Alt. Moon's L. L. 68° 21' 00" 
N. Dip. 26 ft. Chronometer read 6h 18' 28" A. M. 



G. M. T. 17d 

Dec. 17d 18h 
Corr. for 18'.5 


18h 18' 28" 


19'.7 S 
3'.1 


increasing 


Dec. for 17d 18h 18'.5 9° 

S. D. 14'.8 H. P. 

Obs. Alt. 68° 
S. D. + 


22'.8 S 
54'.4 

21' 00" 

14' 48" 




Dip 


68° 


35' 48" 
5' 00" 




Par. and Ref . 


68° 


30' 48" 
19' 34" 




True Alt. 


68° 
90° 


50' 22" 
00' 00" 


N 


Z. D. 

Dec. 


21° 
9° 


09' 38" 
22' 48" 


S 
S 


Lat, 


30° 


32' 26" 


S 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 229 



PROBLEM NO. 3 

July 4, 1919. Obs. Mer. Alt. Moon's L. L. 24° 18' 30" S, 
Dip 26 ft. Chronometer read 3h 12' 18" P. M., slow 4' 18", 



Chron. 
Slow 


3h 12' 18" 

+ 4' 18" 


G. M. T. 4d 

Dec. 4d 2h 
Corr. Ih 16' 


3h 16' 36" 

6° 09'.7 S increasing 
13'.6 


Dec. 4d 3h 16' 

S. D. 15'.0 

Obs. Alt. 
S. D. 


6° 
H. P. 

24° 


23'.3 S 

55' 

18' 30" 
15' 00" 


Dip 


24° 


33' 30" 
5' 00" 


Par. and Ref. 


24° 

+ 


28' 30" 

47' 58" 


True Alt. 


25° 

90° 


16' 28" S 
00' 00" 


Z. D. 

Dec. 


64° 
6° 


43' 32" N 
23' 18" S 


Lat. 


58° 


20' 14" N 



230 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 4 

May 21, 1919. Obs. Mer. Alt. Moon's L. L. 82° 10' 13" S. 
Dip 26 ft. Chronometer read lOh 18' 26" A. M., slow 4' 

18". 



Chron. 
Slow 


22h 18' 26" 
-h 4' 18" 


G. M. T. 20d 


22h 22' 44" 


Dec. 20d 22h 
Corr. 23' 


12° 47'.2 S decreasing 
3'.7 


Dec. 20d 22h 23' 


12° 43'.5 S 


S. D. 15'.4 


H. P. 56'.5 


Obs. Alt. 
S. D. 


82° 10' 13" S 
+ 15' 24" 



82° 25' 37" 
Dip - 5' 00" 



82° 20' 37" 
Par and Ref. + 7' 24" 



True Alt. 82° 28' 01" S 

90° 00' 00" 



Z. D. 7° 31' 59" N 

Dec. 12° 43' 30" S 



Lat. 5° 11' 31" S 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 231 



PROBLEM NO. 5 

Apr. 18, 1919. Obs. Mer. Alt. Moon's L. L. 46° 58' 
12" N. Dip 28 ft. Chronometer read 6h 18' 16" P. M., 
slow 48' 12". 



Chron. 

Slow 


6h 18' 16" 

. + 48' 12" 




G.M.T.lSd 

Dec. 18d 6h 
Corr. Ih 06' 


7h 06' 28" 

2r 01'.2 S 
2'.8 


increasing 


Dec. 18d 7h 06' 

S. D. 14'.8 

Obs. Alt. 
S. D. 


21° 
H. P. 

46° 

+ 


04'.0 S 

54'.2 

58' 12" 
14' 48" 


N 


Dip 


47° 


13' 00" 
5' 11" 




Par. and Ref. 


47° 

4- 


07' 49" 
35' 59" 




True Alt. 


47° 
90° 


43' 48" 
00' 00" 




Z. D. 

Dec. 


42° 
21° 


16' 12" 
04' 00" 


S 
S 


Lat. 


63° 


20' 12" 


S 



232 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 6 

Dec. 6, 1919. Obs. Mer. Alt. Moon^s L. L. 82° 28' 
36" S. Dip 18 ft. Chronometer read 2h 16' 28" A. M., 
fast 34' 18". 



Chron. 

Fast 


14h 16' 28" 
34' 18" 




G.M.T.Sd 

Dec 5d 12h 
Corr. Ih 42' 


13h 42' 10" 

18° 38'.1 N 
10'.5 


increasing 


Dec. 5d 13h 42' 

S. D. 16'.7 

Obs. Alt. 
S. D. 


18° 
H.P. 

82° 


48'.6 N 

61'.2 

28' 36" 
16' 42" 




Dip 


82° 


45' 18" 
4' 09" 




Par. and Ref. 


82° 


41' 09" 

7' 41" 




True Alt. 


82° 
90° 


48' 50" 
00' 00" 


S 


Z. D. 
Dec. 


7° 
18° 


11' 10" 

48' 36" 


N 
N 


Lat. 


25° 


59' 46" 


N 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 233 



TIME OF MOON'S MERIDIAN PASSAGE 

PROBLEM NO. 1 

Jan. 28, 1919. Find Meridian Passage of Moon in 
Long. 84° 24' W. 

Long, in time 5h 37' 36" 

Moon's Transit (N. A.) 28d 22h 00' Diff. 52 

Corr. Table IV W or + 12' 



Mer. Passage 22h 12' or 

lOh 12' A. M. 

PROBLEM NO. 2 

Feb. 7, 1919. Find Meridian Passage of Moon in Long. 
128° 14' E. 

Long, in Time 8h 32' 56" 

Moon's Transit 7d 5h 50' Diff. 57 

Corr. Table IV E or - 21' 



Mer. Passage 5h 29' P. M. 

PROBLEM NO. 3 

Mar. 10, 1919. Find Meridian Passage of Moon in 
Long. 178° 23' W. 

Long, in Time llh 53' 32" 

Moon's Transit lOd 7h 34' Diff. 53 

Corr. Table IV W or -f 27' 



Mer. Passage 8h 01' P. M. 

PROBLEM NO. 4 

Apr. 8, 1919. Find Meridian Passage of Moon in 
Long. 8° 16' E. 

Long, in Time 33' 04" 

Moon's Transit 8d 7h 15' Diff. 48 

Corr. Table IV E or - 1' 



Mer. Passage 7h 14' P. M. 



234 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 5 

June 16, 1919. Find Meridian Passage of Moon in 
Long. 110° 18' W. 

Long, in Time 7h 2V VI" 

Moon's Transit 16d 14h 44' Diff. 48 

Corr. Table IV W or + 14' 



Mer. Passage 14h 58' or 

2h 58' A. M. 



PROBLEM NO. 6 

July 11, 1919. Find Meridian Passage of Moon in 
Long. 156° E. 

Long, in Time lOh 24' 

Moon's Transit lid llh 00' Diff. 51 

Corr. Table IV E or - 22' 



Mer. Passage lOh 38' P. M. 



CHAPTER XIX 
LONGITUDE BY SUNRISE AND SUNSET OBSERVATIONS 

This problem is to find the longitude when the Sun^s 
upper or lower limb just touches the horizon at sunrise or 
sunset. 

It is only necessary to use a pair of marine glasses for 
this observation, and the chronometer must be read at 
instant of contact with horizon. 

As it is very doubtful that a proper contact with sun and 
horizon has been noted, this observation is not to be reUed 
upon, but the navigator should understand it, as it is often 
the case that he does not get any sights during the day and 
the sun sets in the clear. He can then get a fairly good idea 
of his longitude from this problem. 

Correct chronometer and find G. M. T. 

Take out declination and equation of time for Green- 
wich date and time. 

Find G. A. T. and polar distance as before. 

Add together latitude and polar distance. 

Subtract 21' from this sum if lower limb was observed. 

Subtract 53' from this sum if upper limb was observed. 

Divide result by 2. Answer will be half sum. 

Add 21' to half sum if lower limb was observed. 

Add 53' to half sum if upper limb was observed. 

Result will be remainder. 

From Table 44 (Bowditch) take out following logs. : 

Secant of latitude. Rejecting 10 from index number. 

Cosecant of polar distance. Rejecting 10 from index 
number. 

Cosine of half sum. 

Sine of remainder. 

Add these four logs, together, and subtract 10 from index 
number. 

Log. haversine that agrees with sum of logs., will be 
L. A. T. 

If the sun was rising look from bottom of page, and date 
one day back. 

If sun was setting look from top of page, and date same 
as example. 

235 



236 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

Apply L. A. T. to G. A. T. as in previous methods for 
longitude, and obtain the longitude of the place. 

These problems in this book will be given with the longi- 
tude by D. R. and the chronometer time as it reads from 
the chronometer. The student must ascertain for himself 
whether the chronometer time is A. M. or P. M. 

Since at low altitude refraction is very indeterminate, 
this method gives only an approximate longitude. 

Taking corrected altitude as —21^ and —53' respectively, 
really assumes that there is no dip. If the observation 
were taken very much above sea level it would be better 
to make further correction for this by adding the correction 
found in Table 14. 

PROBLEM NO. 1 

Jan. 11, 1919, Sun's L. L. at sunset observed. Chron. read llh 03' 12" 
which was slow on Dec. 6th, 15' 28" and gaining 4".7 daily. D. R. Lat. 
18° 14' N. D. R. Lons. 96° E. 



Chron. 
Slow 


23h 03' 12" 

-f 15' 28" 


Interval 36 di 
Rate 4". 7 

169" = 

Dec. lOd 22h 
Corr. 

Dec. 

P.D. 

Sec 

42" Csc 


lys 


Ace. Rate 


23h 18' 40" 
2' 49" 


=2' 49" ace. rate 

21° 56'.2 S 
0'.5 


G. M. T. lOd 

Eq. Tune 


23h 15' 51" 

7' 45" 


21° 55'.7 S 
90° OO'.O 


G. A. T. lOd 


23h 08' 06" 

18° 14' 
111° 55' 


Lat. 
P.D. 


111° 55'.7 

.02237 
.03261 



130° 09' 42" 
21' 

2)129° 48' 42" 



Rem. 



64° 


54' 
21' 


21" 


Cos 

Sin 

Log. Hav. 

5h3r 
23h 08' 


06" 
06" 


9.62748 




65° 


15' 


21" 


9.95812 


L. A. T. lid 
G. A. T. lOd 


9.64058 


Long. 


6h23' 
95° 45' 


00" 
E 


or 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 237 



PROBLEM NO. 2 

Feb. 23, 1919, Sun's upper limb at sunset observed. Chron. read 
llh 18' 26" which was slow on Jan. 10th, 58' 12" and loses 7".2 daily. 
D. R. Lat. 29° 28' N. Long. 96° 50' W. 



Chron. 
Slow 


llh 18' 26" 
4- 58' 12" 


Interval 
Rate 

Dec. 23d ] 

Corr. .4h 

Dec. 

P.D. 

Sec 
12" Csc 


44.5 days 

7".2 


Ace. Rate 


12h 16' 38" 
-f- 5' 20" 


320" 
i2h 


'=-5' 20" ace. rate 

9° 55'.6 S 
0'.4 


G. M. T. 23d 

Eq. Time 


12h 21' 58" 
13' 33" 


9° 55'.2 
90° OO'.O 


G. A. T. 23d 


12h 08' 25" 

29° 28' 
99° 55' 


Lat. 
P.D. 


99° 55'.2 

.06016 
.00654 



129° 23' 
53' 


12" 


2)128° 30' 


12" 


64° 15' 
+ 53' 


06" 



Cos 9.63791 

Rem. 65° 08' 06" Sin 9.95775 



Log. Hav. 9.66236 



L. A. T. 23d 5h 41' 27' 

G. A. T. 23d 12h 08' 25' 



Long. 6h 26' 58" or 

96° 44' 30" W 



CHAPTER XX 
PHI PRIME SIGHT FOR LATITUDE 

This is only good when sun or star is within three hours 
of the meridian, and declination is greater than 3°. 

The D. R. longitude when sight is taken as well as the 
chronometer time are necessary. From the chronometer 
time (G. M. T.) by applying the equation of time and longi- 
tude the local apparent time is found. The hour angle or 
time before or after local apparent noon is then known and 
changed into degrees. 

The declination is found from the Nautical Almanac for 
the G. M. T. of sight. 

The altitude is corrected in the usual manner. 

By adding the log. sec. of the hour angle to the log. tan. of 
the declination ; the log. tan. of an angle named </>'' is found. 

Adding the log. esc. of the declination, the log. sin. of the 
corrected altitude and the sin. of the angle <i>'\ the cos. of an 
angle called 4>' is found. 

(I)" is same name N or S as declination. 

4>' is same name as Z. D. or opposite from bearing. 

If both same name latitude is the sum of the two angles 
and of same name. 

If of different names latitude is the difference and takes 
name of larger. 

PROBLEM NO. 1 

Jan. 31, 1919. D. R. position 9° 10' S, 46° 15' W. Chron. time 5h 16' 
13". Obs.Alt.Sun'sL.L. 60° 10' 20", bearing SXW. Dip 36'. 

G. M. T. 31d 5h 16' 13" Obs. Alt. 60° 10' 20" 

Eq. Time - 13' 31" Con. + 9' 54" 



G. A. T. 5h 02' 42" Corr. Alt. 60° 20' 14" 
Long. 3h 05' 00" 

Dec. 31d 4h 17° 32'.8 S 

L. A. T. 31d Ih 57' 42" Corr. 1.3h - 0'.9 



Dec. 31d 5.3h 17° 31'.9 S 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 239 



H.A. 

Dec. 

h 


29° 25' 30" 
17° 3r 54" 
60° 20' 14" 

19° 56' 09" S 

10° 24' 00" N 


Sec 
Tan 

Tan 


.05999 
9.49956 


Csc 

Sin 

Sin 
Cos 


.52110 
9.93900 


0" 


9.55955 


9.53271 


r 


9.99281 


Lat. 


= 9° 32' 09" S 





PROBLEM NO. 2 

July 5, 1919, A. M., at ship. D. R. position 27° 00' S, 64° 50' E. Chron* 
Time July 4, 18h 32' 14". Obs. Alt. 37° 10', bearing NXE. Dip 36 ft. 

G. M. T. 4d ISh 32' 14" Obs. Alt 37° 10' 00" 

Eq. Time - 4' 09" Corr. + 8' 43" 



G. A. T. 4d 18h 28' 05" True Alt. 37° 18' 43" 

Long. 4h 19' 20" 

Dec. for 4d 18h 22° 53'.5 N 

L. A. T. 4d 22h 47' 25" Corr. .5h O'.l 

H.A. =lh 12' 35" or 



18° 08' 45" Dec. for 4d 18.5h 22° 53'.4 N 

H.A. 18° 08' 45" Sec .02215' 

Dec. 22° 53' 24" Tan 9.62553 Csc .41009 

h 37° 18' 43" Sin 9.78256 

0" 23° 57' 20" N Tan 9.64768 Sin 9.60856 



60° 44' 56" S Cos 9.80121 



Lat. 26° 47' 36" S 

PROBLEM NO. 3 

Aug. 8, 1919, A. M. at ship. D. R. position 49° 40' N, 178° 12' E 
Chron.timel0h04'03". Obs. Alt. 47° 16' 20", bearing SXE. Dip 36 ft; 

G. M. T. 7d lOh 04' 03" Obs. Alt. 47° 16' 20" 

Eq. Time - 5' 41" Corr. (46) + 9' 09" 



G. A. T. 9h 58' 22" True Alt. 47° 25' 29" 

Long. llh 52' 48" 

Dec. for 7d lOh 16° 32'.4 N 



L. A. T. 7d 21h 51' 10" Corr. for .Ih - O'.l 

H. A. = 2h 08' 50" or — 

32° 12' 30" Corr. for 7d lO.lh 16° 32'.3 N 

H. A. 32° 12' 30" Sec .07257 

Dec. 16° 32' 18" Tan 9.47267 Csc .54594 

h 47° 25' 29" Sin 9.86711 



<!>" 19° 20' 18" N Tan 9.54624 Sin 9.52002 

0' 31° 00' 00" N 

Cos 9.93307 



Lat. 60° 20' 18" N 



CHAPTER XXI 
SUMNER'S METHOD 

This method of finding the ship's position by Sumner 
lines is most generally used when a ship has been running 
several days without observations, and the dead reckoning 
position is doubtful. 

There are various methods used in plotting Sumner lines, 
but the most accurate of these, and one that can be easily 
proved to be correct, is the method of using two assumed 
latitudes. 

Proceed as follows : 

Take an observation of sun or star, and find the longitude 
of two places by working this observation with the 2 as- 
sumed latitudes (a separate calculation with each latitude). 

After obtaining the two positions, place them on the 
chart and connect them together with a line. This will give 
the first line of bearing, and the ship must be somewhere on 
this line if observation was correct. This line will be at 
right angles to sun's true bearing, and can be proved by 
entering azimuth table and obtaining true bearing at time 
of observation. 

After the sun has changed its bearing about 20° take 
another observation, and find the longitude of two places, 
using the same assumed latitudes that were used to work 
first observation. 

Place the two positions found on chart and connect them 
together with a fine. This will give second line of bearing, 
which can be proved by azimuth table as before. 

From first line of bearing allow the course and distance the 
ship has run in the interval between the two observations 
and draw a line parallel to the first line through the position 
found after course and distance has been allowed. This will 
be known as the first line of bearing projected. 

Where the projection of the first line crosses the second 
line of bearing, will be ship's position at time of second obser- 
vation. 

240 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 241 

This problem is accurate if no mistake has been made in 
allowing the proper course and distance between observa- 
tions, and the observed altitude of each is correct. 

The assumed latitudes are generally reckoned 30 miles 
on each side of latitude by dead reckoning. 



PROBLEM NO. 1 (See Illustration) 

Dec. 16, 1919, A. M. at ship. When not sure of ship's position and 
Obs. Alt. of Sun's L. L. read 8° 16' 40". Dip 31 ft. Chron. read llh 
18' 12" A. M., which was fast on Nov. 6th, 8' 48" and losing 8".2 daily. 
Same day later in A. M. the Obs. Alt. Sun's L. L. was 18° 16' 40". Chron. 
read Oh 43' 15" P. M. 

Ship was assumed to be between lats. of 40° and 41° N. Ship run 
between observations N 56° W (true) 46 miles. 



Chron. 
Fast 


First 01 

23h 18' 12" 

- 8' 48" 


bservation 

Interval 
Rate 

Dec. 
P. D 

40" 
18" 


40 ds 

8."2 

328"= 


tys 


Ace. Rate 


23h 09' 24" 

+ 5' 28" 


=5' 28" ace. rate 
23° 17'.1 S 
90° OO'.O 


G. M. T. 15d 

Eq. Time 


23h 14' 52" 
+ 4' 42" 


113° 17'.1 


G. A. T. 15d 

Obs. Alt. 
S. D. 


23h 19' 34" 

8° 16' 
+ 16' 





8° 32' 58' 
Dip - 5' 27' 



8° 27' 31' 
R. & P. - 6' 05' 



True Alt. (h) 

Lat. 

P. D. 


8° 21' 26" 
40° 
113° 17' 06" 


Sec 
Csc 

Cos 

Sin 


.11575 
.03690 


s 
s-h 


2)161° 38' 32" 

80° 49' 16" 

72° 27' 50" 


9.20282 
9.97933 



L. A. T. 15d 20h 18' 21" 
G. A. T. 15d 23h 19' 34' 



Log. Hav. 9.33480 



Long. 3h 01' 13" or 45° 18' 15" W 



242 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



True Alt (h) 

Lat. 

P.D. 



i-h 



8° 21' 26" 
41° 
113° 17' 06" 


Sec 
Csc 


2)162° 38' 32" 




81° 19' 16" 
72° 57' 50" 


Cos 

Sin 



L.A. 
G.A. 

Long. 



T. 15d 20h 22' 52' 
T. 15d 23h 19' 34' 



Log. Hav. 



2h 56' 42" or 44° 10' 30" W 



.12222 
.03690 



9.17867 
9.98051 

9.31830 



Position for First Line 



Dip 



R.&P. 



Lat. 40° N. 
Lat. 41° N. 

Chron. 
Fast 


Long. 45° 18' 15" W. 
Long. 44° 10' 30" W. 

Second Observation 

Oh 43' 15" Dec. 

- 8' 48" 


Ace. Rate 


Oh 34' 27" 
+ 5' 28" 


P.D. 


G.M.T.16d 
Eq. Time 


Oh 39' 55" 
+ 4' 40" 




G. A. T. 16d 

Obs. Alt. 
S.D. 


Oh 44' 35" 

18° 16' 
+ 16' 


40" 
18" 



18° 32' 58" 

- 5' 27" 

18° 27' 31" 

- 2' 44" 



23" 17'.4 S 
90° OO'.O 

113° 17'.4 



True Alt 

Lat. 

P.D. 








18° 24' 47" 
40° 
113° 17' 24" 


Sec 
Csc 




2)171° 42' 11" 




s 
8*h 








85° 51' 06" 
67° 26' 19" 


Cos 
Sin 




L. A. T. 
G. A. T. 


15d 21h 36' 26" 
16d Oh 44' 35" 


Log 



.11575 



8.85938 
9.96543 

8.97747 



Long. 



3h 08' 09" or 47*' 02' 15" W 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 243 



.12222 
.03691 



True Alt. (h) 

Lat. 

P.D. 


18° 24' 47" 
41° 
113° 17' 24" 


Sec 
Csc 




2)172° 42' 11" 




s 
s-h 


86° 21' 06" 
67° 56' 19" 


Cos 
Sin 


L. A. T. 
G. A. T. 


15d 21h 44' 20" 
16d Oh 44' 35" 


Log. 



Long. 3h 00' 15" or 45° 03' 45" W 

Positions for Second Line 

Lat. 40° N. Long. 47° 02' 15" W. 
Lat. 41° N. Long. 45° 03' 45" W. 



8.80368 
9.96698 

8.92979 



CHAPTER XXII 

MARCQ ST. HILAIRE METHOD OR COSINE— HAVER- 
SINE FORMULA 

This is a new method of plotting position Hnes on the 
chart and reduces the amount of figures used in Sumner's 
method considerably. 

The position of the ship by dead reckoning must always 
be used to work from, and in the case where a course and 
distance is given in the interval between observations, the 
latitude and longitude by D. R. must be found for second 
observation before working problem. 

Proceed as follows : 

Correct chronometer and find G. M. T. 

In case of the sun observed, proceed as follows: 

Apply equation of time to G. M. T. and find G. A. T. 

Apply longitude in time to G. A. T. as follows : 

Longitude east, add. 

Longitude west, subtract longitude in time from G. M. T. 

Result will be local apparent time. 

If L. A. T. is over 12 hours, subtract it from 24 hours and 
result will be Sun's hour angle. 

In case of Moon, Star or Planet proceed as follows : 

Apply longitude in time to G. M. T. as before, and obtain 
local mean time. 

Add to L. M. T. the Sun's right ascension from Page 2 
(Almanac) and correction from table below on same page 
for G. M. T. 

Result will be local siderial time. 

From L. S. T. subtract right ascension of body observed. 

Result will be hour angle of body. 

In all cases proceed as follows : 

Take out declination of body observed. 

Correct observed altitude of body observed, and find 
true altitude. 
From Table 45 (Bowditcb) take out log. hav. of body's 
hour angle. 

244 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 245 

From Table 44 (Bowditch) take out log. cos. of latitude 
by D. R. 

From Table 44 (Bowditch) take out Log. Cosine of 
Declination. 

Add these three logarithms together, and subtract 20 
from index Number. 

Opposite the Log. Haversine corresponding to sum of 
logarithms read the natural haversine. 

If latitude and declination are same name, subtract less 
from greater. 

If latitude and declination are different name, add the 
two. 

Take out the Nat. Haversine of this result, and add to it 
the Nat. Haversine obtained already. 

Nat. Haversine corresponding to the sum of the two, will 
be the zenith distance read from top of page (Table 45) in 
degrees, minutes and seconds. 

Subtract zenith distance from 90°. Result will be com- 
puted altitude. 

Under computed altitude, put down true altitude, and 
subtract less from greater. Answer will be altitude differ- 
ence or intercept. 

If the true altitude is greater than computed altitude, 
measure from the dead , reckoning position on the line of 
azimuth toward the body a distance equal to the altitude 
difference or intercept, and draw the position hne through 
this point at right angles to true bearing. 

If true altitude is less than computed altitude measure 
away from body. 

In using the signs, +means toward the body, —means 
away from body. 

Pick out true bearing of body from azimuth table or 
line of position table, which will explain itself. 

If the ship has made any change of position between ob- 
servations, the true course and distance must be allowed 
from first to second sight, and a line drawn parallel to the 
first line on this course and distance crossing the second 
line, will be the ship's position at time of second observation. 

A little practice with this method will convince the stu- 
dent that it is very convenient and simple. 

The position lines will be on the same principle as Sum- 
ner lines, the only difference between the two being the sav- 
ing in time and figures for making the calculations. 



246 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

PROBLEM NO. 1 

Dec. 16, 1919, A. M. at ship. Ship's position by D. R. Lat. 40° 27' N. 
Long. 44° 40' W. Obs. Alt. Sun's L. L. 8° 18' 25". Chron. read llh 18' 
28" A. M. Ship then ran until chron. read Oh 43' 28" P. M. on a course 
N 56° W (true) 46 miles. Obs. Alt. Sun's L. L. 18° 18' 25". Chron. was 
fast on Greenwich time 3' 20". Dip 31 ft. First observation, D. R. 
position 40° 27' N., 44° 40' W. 
Dec. 16, 1919, A. M. 



Chron. 15d 
Fast 


23h 18' 28" 
- 3' 20" 


Dec. 

Obs. Alt. 
Corr. (46) 

True Alt. 

Lat. 
Dec. 

Sum 


23° 17' 12" 1 

8° 18' 25" 
+ 4' 20" 


G. M. T. 

Eq. Time 


23h 15' 08" 
+ 4' 42" 


8° 22' 45" 

40° 27' 00" 
23° 17' 12" 


G. A. T. 

Long. 


23h 19' 50" 
2h 58' 40" 


L. A. T. 


20h 21' 10" 


63° 44' 12" 



Log. Hav. 20h 21' 10" =9.32455 
Log. Cos. 40° 27' =9.88137 

Log. Cos. 23° 17' 12" =9.96310 



Log. Hav. 


9.16902 
9. 16902 = Nat. Hav. 
Nat. Hav. 63° 44' 12" 

Nat. Hav. 

90° 00' 00" 
81° 31' 30" 


.14758 

.27875 


Z. D. 


.42633 = 81° 31 

Bearing of Su 
(from ] 


Com. Alt. 
True Alt. 


8° 28' 30" 
8° 22' 45" 



30" Z. D. 



Alt. Diff. - 5' 45" 

First Obs. D. R. Lat. 40° 27' 00" N 

Course N 56° W, Dist. 46, Diff. Lat. 25' 42" N 



Second Obs. D.] 
First Obs. D. R 
Dep. 38.1, Mid. 


a. Lat. 
. Long. 
Lat. 41°, Diff. Long. 

R. Long. 

Oh 43' 28" 
3' 20" 


40° 52' 42" N 

Dec. 16d Oh 
Corr. 0.7h 

Dec. 16d 0.7h 


44° 40' 00" W 
50' 30" W 


Second Obs. D. 

Chron. 

Fast 


45° 30' 30" W 
23° 17',3 S 
+ O'.l S 


G.M.T, 16d 
Eq. Time 


Oh 40' 08" 
+ 4' 40" 


23° 17'.4 S 


G. A. T. 16d 

Long. 


Oh 44' 48" 
3h 02' 02" 




L.A.T. 


21h 42' 46'^ 





SIMPLE RULES AND PROBLEMS IN NAVIGATION 247 



Log. Hav. 21h 42' 46" 
Log. Cos. 40° 52' 42" 


8.93948 

9.87858 

9.96311 


Obs. Alt. 
Corr. (46) 

True Alt. 

Lat. 
Dec. 

Sum 

:2 

3 

.5 = 71° 38' 

90° 
71° 


18° 18' 
+ 7' 


25" 

45" 


Log. Cos. 23° 17' 24" 


18° 26' 

40° 52' 
23° 17' 


10" 


Log. Hav. 


8.78117 

.0604 

.2821 


42" 
24" 


Log. Hav. 8.781 17 = Nat. Hav. 
Nat. Hav. 64° 10' 06" 


64° 10' 

30" Z. D. 

00' 00" 

38' 30" 


06" 


Nat. Hav. 

Z.D. 


.3425 




Com. Alt. 
True Alt. 


18° 
18° 


21' 30" 
26' 10" 





Alt. Diff. + 4' 40" 

Bearing of Sun N 146° 54' E or S 33° E (from H. 0. 71). 

PROBLEM NO. 2 
SIMULTANEOUS OBSERVATION OF TWO FIXED STARS 

Apr. 16, 1919, P. M. Position by D. R. Lat. 37° 14' N. Long. 
76° 04' W. 

Chron. read 7h 05' 45" P. M. Sirius in the West. Alt. 29° 29'. 

Chron. read 7h 07' 45" P. M. Capella in the West. Alt. 50° 14'. 
Chron. was slow 5h 00' 01". Dip 41 ft. 



Chron. 
Slow 

G. M. T. 16d 
R. A. M. S. 


Sirius in the W( 

7h 05' 45" 
4- 5h 00' 01" 

12h 05' 46" 
Ih 34' 19" 

1' 59" 


3St 

Dec. 

Lat. 
Dec. 

Obs. Alt. 
Corr. (46) 
True Alt. 


16° 36'.6 S 

37° 14' 00" N 
16° 36' 36" S 


Corr. 


53° 50' 36" 


G. S. T. 16d 
Long. 


13h 42' 04" 
5h 04' 16" 


29° 29' 00" 


L. S. T. 16d 


8h 37' 48" 
6h 41' 36" 


8' 00" 


*'s R. A. 


29° 21' 00" 


*'s H. A. 


Ih 56' 12" 





248 SIMPLE RULES AND PR0BLE:\IS IN NAVIGATION 

Log. Hav. Ih 56' 12" = 8.79866 
Log. Cos. 37° 14' =9.90101 
Log. Cos. 16° 36' 36" = 9. 98149 



Log. Hav. 

Log. Hav. 8.( 
Nat. Hav. 53 


8 

38116 = Nat. H 

1° 50' 36" 

90° 00' 
60° 23' 


.68116 

:av. .04799 
.20499 


)° 23' 30" Z 

' W 

45° 55' 

37° 14' 
45° 55' 




Nat. Hav. 
Z. D. 


. 25298 = 6C 
00" 
30" 


. D. 


Comp. Alt. 
True Alt. 


29° 36' 
29° 21' 


30" 
00" 




Alt. Diff. 

First Chron. Time 
Second Chron. Time 


15' 

Capella in tl 

7h 05' 45" 

71i 07' 45" 


30" Az. S 32= 

le West 
Dec. 

Lat. 
Dec. 

Obs. Alt. 
Corr. (46) 

True Alt. 

0745 
0573 


.1 N 


Interval 
First L. S. T. 


2' 
8h 37' 48" 


00" N 
06" N 


Second L. S. T. 
*'s R. A. 


8h 39' 48" 
5h 10' 44" 


8° 41' 

50° 14' 

7' 


06" 


*^s H. A. 


Sh 29' 04" 

= 9.28782 
= 9.90101 
= 9.84241 


00" 
06" 


Log. Hav. 3h 29' 04" 
Log. Cos. 37° 14' 
Log. Cos. 45° 55' 06" 


50° 06' 

X)" Z. D. 
W 


54" 


Log. Hav. 

Log. Hav. 9. 03124 = Nat 
Nat. Hav. 8° 41' 06" 


9.03124 

:. Hav. . 1 
.0 




Nat. Hav. 

Z. D. 


.1 

90° 00' 00' 
39° 19' 00' 


1318 = 39° 19' ( 
' Az. N 59° 




Comp. Alt. 
True Alt. 


50° 41' 00' 
50° 06' 54' 




Alt. Diff. 


34' 06' 





SIMPLE RULES AND PROBLEMS IN NAVIGATION 249 



PROBLEM NO. 3 
POSITION BY OBSERVATION OF THREE FIXED STARS 

Ship stationary between observations. 

May 18, 1919, P. M. Position by D. R. Lat. 40° 40' N. Long. 69° W. 
Chron. read 7h 34' 37" P. M. Star Polaris. Alt. 39° 42' 30". 
Chron. read 7h 36' 58" P. M. Star Vega in the East. Alt. 16° 23' 30". 
Chron. read 7h 38' 55", P. M. Star Capella in the West. Alt. 22** 
48' 24". 

Chron. slow 4h 59' 27". Dip 41 ft. 



Polaris 



Chron. 
Slow 

G. M. T. 18d 

Long. 

L. M. T. 18d 
R. A. M. S. 
Corr. 

L. S. T. 



7h 34' 37" 

+ 4h 59' 27" 



12h 34' 
4h36' 


04" 


7h58' 

3h40' 

2' 


04" 
29" 
04" 



Obs. Alt. 
Corr. (46) 

True Alt. 
Corr. (I) 

Lat. 



39° 42' 30" 

- 7' 26" 

39° 35' 04" 
+ 59' 42" 

40° 34' 46" N 



Uh 40' 37" 



Azimuth 0* 



Fu-st Chron. 
Second Chron. 

Interval 
First L. S. T. 

Second L. S. T. 
*'s R. A. 

*'s H. A. 



7h 34' 37" 

7h 36' 58" 

2' 21" 
llh 40' 37' 

llh 42' 58" 
18h 34' 14" 

6h 51' 16" 



Vega in the East 
Dec. 



Log. Hav. 6h51'16" =9.78598 
Log. Cos. 40° 40' =9.87996 

Iiog. Cos. 38° 42' 24" =9.89229 



Obs. Alt 
Corr. (46) 

True Alt. 

Dec. 

Lat. 



38° 42'.4 

16° 23' 30" 

9' 30" 

16° 14' 00" 

38° 42' 24" N 
40° 40' N 

1° 57' 36" 



I og. Hav. 



9.55823 



Log. Hav. 9.55823 = Nat. Hav. .36159 
Nat. Hav. 1° 57' 36" .00029 



Nat. Hav. 



.36188 = 73° 57' 45" Z. D. 



250 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



Z.D. 


34' 
40' 
55' 


90° 00' 00" 
73° 67' 45" 


I the West 
Dec. 

Lat. 

Obs. Alt. 
Corr. (46) 

True Alt. 


45° 
40° 




Comp. Alt. 
True Alt. 


16° 02' 15" 
16° 14' 00" 




Alt. biff. 

First Chron. 
Third Chron. 


-f- 11' 45" 

Capella in 
7h 34' 37" 
7h 38' 55" 


55' N 
40' N 


Interval 
First L. S. T. 


4' 18" 
llh 40' 37" 


5° 
22° 


15' 

48' 24" 
8' 31" 


Third L. S. T. 
*'s R. A. 


llh 44' 55" 
5h 10' 43" 


22° 


39' 53" 


*'s R. A. 

Log. Hav. 6h 
Log. Cos. 40° 
Log. Cos. 45° 


6h 34' 12" 

12" =9.75917 
= 9.87996 
= 9.84242 





Log. Hav. 9.48155 

Log. Hav. 9. 48155= Nat. Hav. .30306 
Nat. Hav. 5° 15' .00210 



Nat. Hav. .30516=67° 04' Z. D. 

90° 00' 00" Position of Vessel: 

Z. D. 67° 04' 00" Lat. 40° 35' 30" N 

Long. 68° 36' 15" W 

Comp. Alt. 22° 56' 00" 

True Alt. 22° 39' 53" 



Alt. Diff. - 16' 07" 

PROBLEM NO. 4 
POSITION BY OBSERVATION OF FOUR FIXED STARS 

Ship stationary during interval of observations. 
May 19, 1919, P. M. Ship's position by D. R. Lat. 37° 50' N. Long. 
74° 00' W. 

Chron. read 7h 46' 47". Capella in the West. Alt. 22° 08'. 

Chron. read 7h 47' 59". Vega in the East. Alt. 14° 03'. 

Chron. read 7h 50' 40". Spica in the East. Alt. 36° 19'. 

Chron. read 7h 52' 16". Procyon in the West. Alt. 25° 11" 

Chron. slow 4h 59' 24". Dip 41 ft. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 251 

Capella in the West 



Chron. 
Slow 


7h 46' 47" 
+ 4h 59' 24" 


Dec. 
Lat. 

Obs. Alt. 
Corr. (46) 

True Alt. 

184 
t97 


45° 55' 
37° 50' 


G. M. T. 19d 
Long. 


12h 46' 11" 
4h 56' 00" 


8° 05' 

22° 08' 00" 
8' 40" 


L. M. T. 
R. A. M. S. 
Corr. 


7h 50' 11" 

3h 44' 26" 

2' 06" 


21° 59' 20" 


L. S. T. 
*'s R. A. 


llh 36' 43" 
5h 10' 43" 




*'s H. A. 

Log. Hav. 6h26' 
Log. Cos. 37° 50' 
Log. Cos. 45° 55' 


6h 26' 00" 

=9.74554 
= 9.89752 
=9.84242 




Log. Hav. 

Log. Hav. 9.48548^ 

Nat. Hav. 8° 05' 


9.48548 
= Nat. Hav. .30^ 
.00^ 




Nat. Hav. 
Z. D. 


.31( 
90° 00' 00" 

67° 46' 00" 


)81=67''46'Z.D. 

Azhnuth N 48° 
the East 
Dec. 
Lat. 

Obs. Alt. 
Corr. 

True Alt. 




Comp. Alt. 
True Alt. 


22° 14' 00" 
21° 59' 20" 




Alt. Diff. 

First Chron. 
Second Chron. 


14' 40" 

Vega in 
7h 46' 47" 
7h 47' 59" 


W 

38° 42' 24" 
37° 50" 


Interval 
First L. S. T. 


1' 12" 
llh 36' 43" 


0° 52' 24" 

14° 03' 
10' 


Second L. S. T. 
*'s R. A. 


llh 37' 55" 
18h 34' 14" 


13° 53' 


*'s H. A. 


6h 56' 19" 



Log. Hav. 6h56'19" =9.79353 
Log. Cos. 37° 50' =9.89752 
Log. Cos. 38° 42' 24" =9.89233 



Log. Hav. 9.58338 

Log. Hav. 9 . 58338 = Nat. Hav. . 38317 
Nat. Hav. 0° 52' 24" .00006 



Nat. Hav. .38323=76° 29' 45" Z. D. 



252 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



Z.D. 


90° 00' 00" 
76° 29' 45" 


Azimuth N 51° E 
a the Ea,st 

Dec. 10° 
Lat. 37° 


44' 
50' 




Comp. Alt. 
True Alt. 


13° 30' 15" 
13° 53' 00" 




Alt. Diff. 

First Chron. 
Third Chron. 


4- 22' 45" 

Spica i] 
7h 46' 47" 
7h 50' 40" 


36" S 

N 


Interval 
First L. S. T. 


3' 53" 
llh 36' 43" 


48° 

Obs. Alt. 36° 
Corr. - 


34' 

19' 

7' 


36" 

00" 
35" 


Third L. S. T. 
*'s R. A. 


llh 40' 36" 
13h 20' 59" 



's H. A. 



Ih 40' 23' 



True Alt. 



36° IV 25' 



Log. Hav. Ih40'23" =8.67394 
Log. Cos. 37° 50' =9.89752 
Log. Cos. 10° 44' 36" =9.99232 



Log. Hav. 8.56378 

Log. Hav. 8. 56378 = Nat. Hav. .03663 
Nat. Hav. 48° 34' 36" . 16913 



Nat. Hav. 
Z.D. 


.2C 
90° 00' 00" 
53° 57' 


)57^ = 53° 57' Z. 

Azimuth S 31 
in the West 
Dec. 
Lat. 

Obs. Alt. 
Corr. 

True Alt. 


D. 

°E 

5° 
37° 




Comp. Alt. 
True Alt. 


36° 03' 00" 
36° 11' 25" 




Alt. Diff. 

First Chron. 
Fourth Chron. 


+ 8' 25" 
Procyon 
7h 46' 47" 
7h 52' 16" 


25' 48" N 
50' 00" N 


Interval 
First L. S. T. 


5' 29" 
llh 36' 43" 


32° 

25° 


24' 12" 

11' 
8' 20" 


Fourth L. S. T. 
*'s R. A. 


llh 42' 12" 
7h 35' 05" 


25° 


02' 40" 


*'s H. A. 


4h 07' 07" 



Log. Hav. 4h07'07" =9.42089 
Log. Cos. 37° 50' =9.89752 
Log. Cos. 5° 25' 48" =9.99804 



Log. Hav. 



9.31645 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 253 

Log. Hav. 9.31645 = Nat. Hav. .20723 
Nat. Hav. 32° 24' 12" .07784 



Nat. Hav. 
Z. D. 


.28507=64° 32' 15" Z. D. 

90° 00' 00" 
64° 32' 15" 


Comp. Alt. 
True Alt. 


25° 27' 45" 
25° 02' 40" 


Alt. Dilf. 


25' 05" Azimuth S 76° W 



Position of vessel; Lat. 37° 55' 15" N 

Long. 73° 28' 45" W. 



PROBLEM NO. 5 
TWO OBSERVED ALTITUDES OF SLTT»S L. L. 

Oct. 18, 1919, A. M. at ship. Position by D. R. Lat. 36° 35' N. 
Long. 70° 35' W. 

Chron. read llh 59' 18". Alt. 11° 51' 30". 
Chron. read Ih 59' 18". Alt. 32° 18' 45". 
Course between sights S 28° E (true) 31 miles. 
Chron. slow 3' 00". Dip. 30 ft. 

Chron. 23h 59' 18" Dec. 9° 20' 06" S 

Slow + 3' 00" Lat. 36° 35' 00" N 



G. M. T. 18d 

Eq. Time 


Oh 02' 18" 
+ 14' 37" 


Obs. Alt. 
Corr. (46) 

Ti-.i/i A1+ 


45° 55' 06" 

11° 51' 30" 
-f 6' 16" 


G. A. T. 18d 

Long. 


Oh 16' 55" 
4h 42' 20" 


11° KT AR't 



L. A. T.:i7d 19h 34' 35" 

Log. Hav. 19h 34' 35" =9.47634 
Log. Cos. 36° 35' 00" =9.90471 
Log. Cos. 9° 20' 06" =9.99421 

Log. Hav. 9.37526 

Log. Hav. 9 . 37526 = Nat. Hav. . 23727 
Nat. Hav. 45° 55' 06" . 15216 



Nat. Hav. .38943=77° 13' 30" Z. D. 

90° 00' 00" 
Z. D 77° 13' 30" 



Comp. Alt. 12° 46' 30' 

True Alt. 11° 57' 46' 



Alt. Diff. - 48' 44" Azimuth S 67° E 



254 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

First Obs. D.R. Lat. 36° 35' 00" N D. R. Long. 70° 35' 00" W 

Diff. Lat. 27' 24" S Diff. Long. 18' 00" E 



Sec. Obs. D.R. Lat. 36° 07' 36" N 

Chron. Ih 59' 18" 
Slow + 3' 00" 


D. R. Long. 

Dec. 
Lat. 

Obs. Alt. 
Corr. (46) 

Tnm A If 


70° 17' 00" W 

9° 21' 54" S 
36° 07' 36" N 


G. M. T. 18d 
Eq.T. 


2h 02' 18" 
+ 14' 38" 


45° 29' 30" 

32° 18' 45" 
■f 9' 14" 


G. A. T. 18d 

Long. 


2h 16' 56" 
4h 41' 08" 


.Q90 97' fiQ'f 



L. A. T. 17d 21h 35' 48" 

Log. Hav. 21h 35' 48" =8.98113 
Log. Cos. 36° 07' 36" =9.90726 
Log. Cos. 9° 21' 54" =9.99417 

Log. Hav. 8.88256 



Log. Hav. 8. 88256= Nat. Hav. .07630 
Nat. Hav. 45° 29' 30" . 14948 



Nat. Hav. .22578=56° 44' 30" Z. D. 

90° 00' 00" 
Z. D. 66° 44' 30" 



Comp. Alt. 33° 15' 30" 

True Alt. 32° 27' 59" 



Alt. Diff. - 47' 31" Azimuth S 43° 30' E 

Position of Vessel: Lat. 36° 33' 30" N. 
Long. 71° 08' 30" W. 



PROBLEM NO. 6 

POSITION BY SIMULTANEOUS OBSERVATION OF TWO 
FIXED STARS 



Dec. 6, 1919. Position by D. R. Lat. 49° 30' N. Long. 14° 00' W. 
Chron. read 7h 31' 21". Regulus in the West. Alt. 48° 41' 00". 
Chron. read 7h 32' 43". Arcturus in the East. Alt. 46° 32' 30". 
Chron. correct. Dip. 26 ft. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 255 



Regulus in the West 



G. M. T. 5d 

Long. 


19h31' 21" 
Oh 56' 


Dec. 
Lat. 

Obs. Alt. 
Corr. (46) 

True Alt. 


12° 21' 24" 
49° 30' 00" 


1^. M. T. 5d 
R. A. M. S. 
Corr. 


18h 35' 21" 

16h 52' 57" 

3' 12" 


37° 08' 36" 

48° 41' 00" 
5' 51" 


L. S. T. 6d 
*'s R. A. 


llh 31' 30" 
lOh 04' 08" 


48° 35' 09" 


*'s H. A. 


Ih 27' 22" 





Log. Hav. Ih27'22" =8.55500 
Log. Cos. 49° 30' =9.81254 
Log. Cos. 12° 21' 24" =9.98982 



Log. Hav. 



8.35736 



Log. Hav. 8. 35736 = Nat. Hav. .02277 
Nat. Hav. 37° 08' 36" .10143 



Nat. Hav. 
Z.D. 


20' 
30' 
35' 


.12^ 

90° 00' 00" 
41° 16' 15" 


120 = 41° 16' 15" Z. D^ 

Azimuth S 33° 30' W 

in the East 

Lat. 49° 
Dec. 19° 


30' 
35' 




Comp. Alt. 
True Alt. 


48° 43' 45" 
48° 35' 09" 




Alt. Diff. 

First Chron. 
Second Chron. 


8' 36" 

Arcturus 

7h 31' 21" 
7h 32' 43" 


00" 
54" 


Interval 
First L. S. T. 


1' 22" 
llh 31' 30" 


29° 

Obs. Alt. 46° 
Corr. (46) - 


54' 

32' 
5' 


06" 

30" 
50" 


Second L. S. T, 
*'s R. A. 


llh 32' 52" 
14h 12' 00" 


46° 


26' 


40" 


*'s R. A. 

Log. Hav. 21h 
Log. Cos. 49° 
Log. Cos. 19° 


21h 20' 52" 

52" =9.06358 

=9.81254 

54" =9.97408 



Log. Hav. 8.85020 

Log. Hav. 8. 85020 = Nat. Hav. .07083 
Nat. Hav. 29° 54' 06" .06655 



Nat. Hav. 



.13738 = 43° 30' 45" Z. D. 



256 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

90° 00' 00" 
Z. D. 43° 30' 45" 



Comp. Alt. 46° 29' 15" 

True Alt. 46° 26' 40" 



Alt. Diff. - 2' 35" Azimuth S 6^ E 

Position of Vessel: Lat. 49° 39' N. 

Long. 13° 57' W. 



CHAPTER XXIIl 
TIME OF HIGH AND LOW WATER 

This problem is to find the time of high and low water at 
any given port. 

The astronomical date must be thoroughly understood 
in this example, and with careful watching of dates and a 
little practice it is very simple. 

From Appendix IV (Bowditch) take out approximate 
longitude of place given, and lunar interval for high and low 
water. 

From Pages 76-77 (Almanac) take out Moon's transit 
for date preceding the example, and the difference between 
it and the transit for date of example. 

From Table 11 (Bowditch) with difference of transit at 
top of page and approximate longitude on side, take out 
correction given and apply it to Moon's transit for date 
preceding example, by rule given in Table 11. 

Result will be Moon's upper transit. 

Add to Moon's upper transit the lunar interval for high 
water. Result will be time of high water in astronomical 
time. 

To convert this into civil time : 

If time is between Oh and 12h. The date will be the 
same as transit was taken for in P. M. To find time of tide 
in P. M. of date of example add to this the change of transit 
between the dates. 

If time is between 12h and 24h. The date will be the 
same as example in A. M., after subtracting 12 hours from it. 

If time is over 24 hours, subtract 24 horn's from it, and 
the date will be the same as example in P. M. 

To find time of low water : 

Add to Moon's upper transit the lunar interval for low 
water. The same rule as before will hold good for finding 
time of low water. 

257 



258 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

As the difference between the morning and evening 
tides is half the Moon's change of transit for that date. 
Proceed as follows: 

If time for high or low water was fomid for A. M., add 
one-half the difference of transit to it, and the result will be 
P. M. time of high or low water. 

If time found was P. M., subtract one-half the difference 
of transit from it, and the result will be A. M. time of high 
or low water. 



PROBLEM NO. 1 

Jan. 18, 1919. Find time of high and low water A. M. 
and P. M. at Montauk Point, N. Y. 

Approximate Long. 72° W. Limar Interval H. W. 
8h 20'. Lunar Interval L. W. 2h 03'. 



Moon's Transit 17th 
Corr. Table 11 

Moon's Upper Transit 
Lunar Int. H. W. 

High y/ater, Jan. 17 

Jan. 18th 
One-half Diff. of Trans. 

High Water, Jan. 18th 

Moon's Upper Transit 
Lunar Int. L. W. 

Low Water, Jan. 17th 
Jan. 18th 
One-half Diff. of Transit 

Low Water, Jan. 18th 



ifference of ' 

13h 30' 
-^ 09' 


Tra 

or 
A. 

P. 

or 
A. 

P. 


msit 46' 


13h 39' 
8h 20' 




21h 59' 

9h 59' 

4- 23' 


M. 


lOh 22' 

]3h 39' 
2h 03' 


M. 


15h 42' 

3h 42' 

-f- 23' 


M. 


4h 05' 


M. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 259 



PROBLEM NO. 2 

July 19, 1919. Find time of high and low water A. M. 
and P. M. at New York Navy Yard, N. Y. 

Approximate Long. 74° W. Lunar Interval H. W. 8h 
44'. Lunar Interval L. W. 2h 49'. 



Difference of Transit 51 



Moon's Transit 18th 16h 43' 

Corr. Table 11 +10' 



Upper Transit 
Lunar Int. H.W. 


16h 53' 
8h 44' 




High Water, July 19th 
One-half Diff. of Trans. 


Ih 37' P. 
26' 


M. 


High Water, July 19th 

Upper Trans. 
Lunar Int. L. W. 


Ih 11' A. 

16h 53' 
2h 49' 


M. 


Low Water, July 18th 
July 19th 
One-half Diff. of Trans. 


19h 42' or 
7h 42' A. 
-F 26' 


M. 



Low Water July 19th 8h 08' P. M, 



260 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 3 

Sept. 13, 1919. Find time of high and low water A. M. 
and P. M. at Aden, Arabia. 

Approximate Long. 45° E. Lunar Interval H. W. 7h 49'. 
Lunar Interval L. W. Ih 41'. 



Difference of Transit 56'. 



Moon's Trans. 12th 
Corr. Table 11 

Upper Trans. 
Lunar Int. H. W. 

High Water, Sept. 12th 
Sept. 13th 
One-half Diff. of Trans. 

High Water, Sept. 13th 

Upper Trans. 
Lunar Int. L. W. 

Low Water Sept 12th 
Sept. 13th 
One-half Diff. of Trans. 

Low Water Sept. 13th 



14h 19' 

07' 


or 
A. 

P. 

or 
A. 

P. 




14h 12' 
7h 49' 




22h or 
lOh or 

+ 28' 


M. 


lOh 29' 

14h 12' 
Ih 41' 


M. 


15h 53' 
3h 53' 

+ 28' 


M. 


4h 21' 


M. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 261 



PROBLEM NO. 4 

Feb. 17, 1919. Find time of high and low water A. M. 
and P. M. at Valparaiso, Chile. 

Approximate Long. 72° W. Lunar Interval H. W. 9h 37'. 
Lunar Interval L. W. 3h 26' 



Moon's Trans. 16th 
Corr. Table 11 

Upper Trans. 
Lunar Int. H. W. 

High Water, Feb. 16th 
Feb. 17th 
One-half Diff . of Trans. 

High Water, Feb. 17th 

Upper Trans. 
Lunar Int. L. W. 

Low Water 16th 

Feb. 17th 
One-half Diff. of Trans. 

Low Water Feb. 17th 



Difference 

13h 37' 
+ 09' 


of 

or 
A. 

P. 

or 
A. 

P. 


Transit 43'. 


13h 46' 
9h 37' 




23h 23' 

llh 23' 

22' 


M. 


llh 45' 

13h 46' 
3h 26' 


M. 


17h 12' 

5h 12' 

22' 


M. 


5h 34' 


M. 



262 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 6 

Aug. 26, 1919. Find time of high and low water A. M. 
and P. M. at Enderbury Island, Phoenix Islands, Islands 
of the Pacific. 

Approximate Long. 171° W. Lunar Int. H. W. 5h 00'. 
Lunar Int. L. W. llh 15'. 

Change of Transit 46'. 

Moon's Trans. 26th Oh 34' 

Corr. Table 11 +22' 



Upper Trans. Oh 56' 

Lunar Int. H. W. 5h 00' 



High Water, Aug. 26th 5h 56' P. M. 

One-half Change of Trans. - 23' 



High Water, Aug. 26th 

Upper Trans. 
Lunar Int. L. W. 

Low Water, Aug. 27 
One-half Change of Trans. 

Low Water Aug. 26th 



5h 33' A. 

Oh 56' 
llh 15' 


M. 


12h 11' A. 
23' 


M. 


llh 48' A. 


M, 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 263 



PROBLEM NO. 6 

July 8, 1919. Find time of high and low water A. M. 
and P. M. at New Bedford, Mass. 

Approximate Long. 71° W. Lunar Interval H.W. 7h 57'. 
Lunar Interval L. W. Ih 18'. 

Change of Transit 47'. 

Moon^s Trans. 7th 7h 45' 

Corr. Table 11 +09' 

Upper Trans. 
Lunar Int. H. W. 

High Water, July 7th 
July 8th 
One-half Change of Trans. 

High Water, July 8th 

Upper Trans. 
Lunar Int. L. W. 

Low Water, July 7th 

Change of Trans. + 

Low Water, July 8th 
One-half Change Trans. — 

Low Water July 8th 9h 35' A. M. 



7h 54' 

7h 57' 




15h 51' or 
3h 51' A. 

24' 


M. 


4h 15' P. 

7h 54' 
Ih 18' 


M. 


9h 12' P. 

47' 


M. 


9h 59' P. 

24' 


M. 



264 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 7 

Dec. 19, 1919. Find time of high water and low water 
A. M. and P. M. at Vardo, Norway. 

Approximate Long. 31° E. Lunar Interval H. W. 
5h 40'. Lunar Interval L. W. llh 57'. 

Change of Transit 48' 

Moon's Trans. 18th 21h 36' 

Corr. Table 11 - 04' 



Upper Trans. 21h 32' 

Lunar Int. H. W. 5h 40' 



27h 12' 
High Water, Dec. 19th 3h 12' P. M. 

One-half Change of Trans. - 24' 



High Water, Dec. 19th 2h 49' A. M. 

Upper Trans. 21h 32' 

Lunar Int. L. W. llh 57' 



Low Water, Dec. 19th 9h 29' P. M. 

One-half Change of Trans. - 24' 



Low Water Dec. 19th 9h 05' A. M. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 265 



PROBLEM NO. 8 

Feb. 4, 1919. Find time of high and low water A. M. 
and P. M. at Calais, Maine. 

Approximate Long. 67° W. Lunar Interval H. W. 1 Ih 36'. 
Lunar Interval L. W. 5h 40'. 



Moon's Trans. Feb. 3d 
Corr. Table 11 

Upper Trans. 
Lunar Int. H. W. 

High Water Feb. 3d 
Feb. 4th 
One-half Change of Trans. 

High Water Feb. 4th 

Upper Trans. 
Lunar Int. L. W. 

Low Water Feb. 3d 
Change of Trans. 



Low Water Feb. 4 

One-half Change of Trans. — 

Low Water Feb. 4 



Change 

2h 18' 
-f- 09' 


!0f 

or 
A. 

P. 

P. 
P. 
A. 


Transit 51' 


2h 27' 
llh 36' 




14h 03' 

2h 03' 

-h 26' 


M. 


2h 29' 

2h 27' 
5h 40' 


M. 


8h 07' 
51' 


M. 


8h 58' 
26' 


M. 


8h 32' 


M. 



266 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 9 

]\Iay 4, 1919. Find time of high and low water A. M, 
and P. 'M. at Christiania, Norway. 

Approximate Long. 11^ E. Lunar Interval H. W. 5h 22'. 
Lmiar Interval L. W. lOh 37'. 



Change of Transit 54' 



Moon's Transit, ]\Iay 4th 4h 15' 

Corr. Table 11 - 02' 



Upper Transit 4h 13' 

Lunar Int. H. W. 5° 22' 



High Water, :\Iay 4th 9h 35' P. M. 

One-half Change of Trans. — 27 






High V^'ater, May 4th 

Upper Trans. 
Lunar Int. L. W. 

Lovn- Water. :May 4th 
I\Iay 5th 

Change of Transit — 

Low Water, ^lay 4th 
One-half Change of Trans, -f 

Low Water, ]May 4th 



9h 08' 

4h 13' 

lOh 37' 


A. 

or 
A. 

A. 

P. 


M. 


14h 50' 

2h 50' 

54' 


M. 


Ih 56' 
27' 


M. 


2h 23' 


M, 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 267 



PROBLEM NO. 10 

Jan. 10, 1919. Find time of high and low water A. M. 
and P. M. at Pernambuco, Picao Lighthouse, Brazil. 

Approximate Long. 35° W. Lunar Interval H. W. 4h 
33'. Lunar Interval L. W. lOh 50'. 



Change of Transit 56' 



Moon's Trans., Jan. 10th 6h 58' 

Corr. Table 11 +05' 



Upper Transit 
Lunar Int. H. W. 


7h 03' 
4h 33' 




High Water, Jan. 10th 
One-half Change of Trans. 


llh 36' P. 

28' 


M. 


High Water, Jan. 10 

Upper Trans. 
Lunar Int. L. W. 


llh 08' A. 

7h 03' 
lOh 50' 


M. 


Low Water, Jan. 10 

Jan 11th 
Change of Trans. 

Low Water, Jan. 10th 
One-half Change of Trans. 


17h 53' or 
5h 53' A. 
56' 

4h 57' A. 
+ 28' 


M, 
M, 



Low Water, Jan. 10th 5h 25' P. M. 



268 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



PROBLEM NO. 11 

Mar. 5, 1919. Find time of high and low water A. M. 
and P. M. at Hilo, Kanaha Point Light, Hawaiian Islands. 

Approx. Long. 155° W. L. I. H. W. 3h 09'. L. I. L. W. 
9h 06'. 



Moon's Transit, Mar. 5th 
Corr. Table 11 


Change of Transit 57' 

2h 47' 
+ 24' 


Upper Transit 
Lunar Int. L.W. 


3h 11' 

3h 09' 


High Water, Mar. 5th 
One-half Change of Trans. 


6h 20' P. M. 

28' 


High Water, Mar. 5th 

Upper Trans. 
Lunar Int. L. W. 


oh 52' A. M. 

3h 11' 

9h 06' 


Low Water, Mar. 6th 
One-half Change of Tarnsit 


I2h 17' A. M. 

28' 


Low Water, Mar. 5th 


llh 49' A. M, 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 269 



PROBLEM NO. 12 

Oct. 26, 1919. Find time of high and low water A. M. 
and P. M. at Osaka, Fort Temposan Light, Japan. 

Approx. Long. 135° E. Lunar Interval H. W. 7h 30'. 
Lunar Interval L. W. Ih 25' 



Change of Transit 48' 



Moon's Transit, Oct. 26th 
Corr. Table 11 

Upper Transit 
Lunar Int. H. W. 

High Water, Oct. 26th 
One-half Change of Trans. — 

High Water, Oct. 26th 

Upper Transit 
Lunar Int. L. W. 

Low Water, Oct. 26th 
One-half Change of Trans. — 

Low Water, Oct. 26th 



Ih 43' 
18' 




Ih 25' 
7h 30' 




8h 55' P. 

24' 


M. 


8h 31' A. 

Ih 25' 
Ih 25' 


M. 


2h 50' P. 
24' 


M. 


2h 26' A, 


M, 



CHAPTER XXIV 
EXAMPLES FOR PRACTICE 



DAY'S WORK 

1. A ship takes her departure from a point in Lat. 32^ 
48' N, Long. 116° IS^W, bearing by compass N 48° E dis- 
tance 16 miles. Ship's head N 20° W, and steers the follow- 
ing courses: 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


N 20° W 


41 


N E 


5° 


6° W 


12° E 


N 80° W 


42 


North 


9° 


8° W 


12° E 


S 45° W 


43 


N W 


8° 


3° W 


12° E 


South 


44 


West 


6° 


8° W 


12° E 


S 20° E 


45 


S W 


T 


3° W 


12° E 


S 15° W 


46 


S E 


4° 


5° W 


12° E 



Current set East (Corr. Mgc.) 14 miles for day. 
Required latitude and longitude arrived at? True course 
and distance made? 



Answer. Latitude in 30° 40' 12" N. Long, in 
04' W. True course S 35° W. Distance 156 miles. 



118' 



2. A ship takes her departure from a point in Lat. 28° 
32' S, Long 28° 10' E, bearing by compass West distance 
14 miles. Ship's head N 10° E, and sails the following 
courses : 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


N 10° E 


41 


N W 


6° 


3° E 


15° W 


East 


42 


North 


7° 


4° E 


15° W 


S 70° E 


43 


N E 


6° 


r E 


15° W 


S 30° E 


44 


East 


7° 


2° W 


15° W 


South 


45 


East 


6° 


4° W 


15° W 


S 10° W 


46 


S E 


2° 


V w 


15° W 



270 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 271 



Current set West (Corr. Mgc.) 30 miles for day. 
Required latitude and longitude arrived at? 
course and distance made? 



True 



Answer.— Latitude in 30° 05' 24" S. Longitude in 30° 
19' 30'' E. True course S 51° E. Distance 146 miles. 

3. A ship takes her departure from a point in Lat. 49° 
58' N, Long. 10° 12' W, bearing by compass N 40° E, dis- 
tance 15 miles. Ship's head N 45° W, and sails the follow- 
ing courses: 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


N 45° W 


38 


North 


6° 


5° E 


24° W 


West 


39 


North 


7° 


9° E 


24° W 


S 78° W 


40 


N W 


8° 


10° E 


24° W 


S 10° w 


42 


West 


9° 


3° E 


24° W 


S 20° E 


43 


s w 


8° 


3° W 


24° W 


South 


44 


s w 


4° 


8° E 


24° W 



Current set S 10° E (Corr. Mgc.) 13 miles for day. 
Required latitude and longitude arrived at? 
course and distance made? 



True 



Answer.- 
11° 11' W. 



-Latitude in 47° 23' 
True course S 14° W. 



42" N. Longitude in 
Distance 159 miles. 



4. A ship takes her departure from a point in Lat. 48° 
10' N, Long. 128° 46' W, bearing by compass West, distance 
10 miles. Ship's head N 28° E, and sails the following 
courses : 



Courses 


Distance 


Wind 


Leeway 


Deviation 


Variation 


N 28° E 


38 


N W 


3° 


4° E 


20° E 


N 28° W 


40 


West 


2° 


3° W 


20° E 


West 


42 


N W 


4° 


5° W 


20° E 


S 48° W 


44 


N W 


5° 


3° W 


20° E 


S 10° w 


46 


West 


3° 


1° W 


20° E 


S 10° E 


48 


s w 


3° 


2° E 


20° E 



Current set East (Corr. Mgc.) 13 miles for day. 
Required latitude and longitude arrived at? True 
course and distance made? 

Answer.— Latitude in 47° 20' 06" N. Longitude in 
130° 17' W. True course S 51° W. Distance 79 miles. 



272 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



U. S. NAVY METHOD 

5. A ship is heading 340° (p. s. c.) Dev. 4° W and takes 
her departure at noon with Point Reyes Lighthouse, CaH- 
fornia, abeam distance 10 miles. Patent log reads 18. 

At 3 P. M. Changed course to 230°. Patent log 57. 
Deviation 2° W. 

At 7 P. M. Changed course lo 180°. Patent log 9. 
Deviation 2° E. 

At 10 P. M. Changed course to 270°. Patent log 45. 
Deviation 3° W. 

At 12 P. M. Changed course to 310°. Patent log 71. 
Deviation 6° W. 

At 4 A. M. Changed course to 360°. Patent log 23. 
Deviation 9° W. 

At 8 A. M. Changed course to 330°. Patent log 72. 
Deviation 8° W. 

At noon patent log read 24. 

Current set 40° (Corr. Mgc.) at rate |' per hour. 

Variation on all courses 22° E. 

Required noon position by dead reckoning, and true 
course and distance? 

Answer.— Latitude in 40° 22' 33'' N. Longitude in 
125° 37' 24" W. True course 320°. Distance 186 miles. 

6. A ship is heading 65° (p. s. c.) Dev. 6° E and takes 
her departure at 7 A. M. with Five Fathom Bank Light- 
ship, New Jersey, abeam. Distance 8 miles. Patent log 
read 0. 

At noon changed course to 120°. Patent log 75. Devi- 
ation 4° E. 

At 4 P. M. Changed course to 180°. Patent log 35. 
Deviation 2° E. 

At 8 P. M. Changed course to 110°. Patent log 94. 
Deviation 5° E. 

At 12 P. M. Changed course to 40°. Patent log 54. 
Deviation 8° E. 

At 4 A. M. Changed course to 0°. Patent log 9. 
Deviation 4° E. 

At 8 A. M. Changed course to 340°. Patent log 67. 
Deviation 2° W. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 273 

At noon patent log read 22, variation on all courses 9° W. 
Current set 310° (Corr. Mgc.) f ' per hour for run. 
Required noon position by dead reckoning, and true 
course and distance made? 

Answer.— Latitude in 40° 13' 50'' N. Longitude in 
70° 50' 36" W. True course 63°. Distance 192 miles. 



MERCATOR'S SAILING 

1. Required true course and distance from Lat. 56° 46' 
N, Long. 150° 00' W, to Lat. 73° 10' N, Long. 168° 10' E by 
Mercator's sailing? 

Answer.— True course N 46° 11' W. Distance 1421 
miles. 

2. Required true course and distance from Lat. 28° 14' 
S, Long. 28° 30' E, to Lat. 40° 10' N, Long. 10° 16' W, by 
Mercator's sailing? 

Ansv/er.— True coiu"se N 27° 59' W. Distance 4647 
miles. 

3. Required true course and distance from Lat. 14° 16' 
S, Long. 28° 00' W, to Lat. 14° 16' N, Long. 28° 00' E, by 
Mercator's sailing? 

Ansv/er.— True course N 62° 55' E. Distance 3760 miles. 

4. Required true course and distance from Lat. 46° 18' 
N, Long. 165° 20' E, to Lat. 23° 28' N, Long. 168° 40' W by 
Mercator's sailing? 

Answer.— True course S 42° 48' E. Distance 1867 miles. 

5. Required true course and distance from Lat. 13° 48' 
S, Long. 113° 28' E, to Lat. 39° 20' N, Long. 74° 30' E, by 
Mercator's sailing. 

Answer.— True course N 34° 37' W. Distance 3874 
miles. 

6. Required true course and distance from Lat. 46° 28' 
S, Long. 18° 46' E, to Lat. 25° 30' S, Long. 22° 23' W by 
Mercator's sailing? 

Answer.— True course N 57° 37' W. Distance 2349 
miles. 



274 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



MIDDLE LATITUDE SAILING 

1. Required true course and distance from Lat. 28° 10' N, 
Long. 76° 15' W to Lat. 34° 12' N, Long. 77° 40' W by 
middle latitude sailing? 

Answer. — True course N 11° W. Distance 369 miles. 

2. Required true coiu-se and distance from Lat. 18° 46' 
S long., 178° 00' W to Lat. 16° 30' S, Long. 175° 10' E by 
middle latitude sailing? 

Answer. — True course N 71° W. Distance 412 miles. 

3. Required true course and distance from Lat. 48° 16' N, 
Long. 2° 06' W, to Lat. 53° 12' N, Long. 0° 42'E, by middle 
latitude sailing? 

Answer. — True course N 20° E. Distance 315 miles. 

4. Required true course and distance from Lat. 38° 10' N, 
Long. 28° 10' W to Lat. 42° 36' N, Long. 31° 9' W by mid- 
dle latitude sailing? 

Answer. — True course N 27° W. Distance 299 miles. 

5. Required true course and distance from Lat. 46° 18' S, 
Long. 153° 28' E to Lat. 49° 30' S, Long. 159° 10' E by mid- 
dle latitude sailing? 

Answer. — True course S 50° E. Distance 298 miles. 

6. Required true course and distance from Lat. 38° 14' N, 
Long. 25° 30' W to Lat. 47° 18' N, Long. 30° 40' W by mid- 
dle latitude sailing? 

Answer. — True coiu-se N 23° W. Distance 591 miles. 



LATITUDE BY MERIDIAN ALTITUDE OF SUN 

1. Jan. 1, 1919. Obs. Mer. Alt. Sun's L. L. was 49'' 
48' 10" S. Dip 26 ft., Long. 94° 18' W. 

Required latitude? 

Answer.— Latitude 16° 58' 23" N. 

2. Feb. 9, 1919. Obs. Mer. Alt. Sun's L. L. was 81° 
10' N. Dip 40 ft. Index error +2'. Long. 57° 43' E. 

Required latitude? 

Answer.— Latitude 23° 35' 53" S. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 275 

3. March 21, 1919. Obs. Mer. Alt. Sun's L. L. was 59^ 
36' S. Index error +2' 40''. Dip 28 ft. Long, by D. R. 
41° 28' E. 

Required latitude? 

Answer.— Lat. 30° 04' 08" N. 

4. Apr. 9, 1919. Obs. Mer. Alt. Sun's L. L. was 48° 
10' N. Dip 26 ft. Long, by D. R. 168° 15' E? 

Required latitude? 

Answer.— Lat. 34° 33' 10" S. 

5. May 6, 1919. Obs. Mer. Alt. Sun's L. L. was 82° 
10' S. Dip. 36 ft. Long, by D. R. 16° 21' W. 

Required latitude? 

Answer.— Lat. 23° 59' 42" N. 

6. June 22, 1919. Obs. Mer. Alt. Sun's L. L. was 51° 
28' N. Dip 26 ft. Long, by D. R. 167° 42' W. 

Required latitude? 

Answer.— Lat. 14° 55' 00" S. 



LATITUDE BY MERIDIAN ALTITUDE OF STAR 

1. Feb. 9, 1919. Obs. Mer. Alt. * Spica 41° 10' S. Dip 
39 ft. 

Required latitude? 

Answer.— Lat. 38° 12' 44" N. 

2. Mar. 11, 1919. Obs. Mer. Alt. *Arcturus28° 19' 
N. Index error -1' 50". Dip 26 ft. 

Required latitude? 

Answer.— Lat. 42° 13' 44" S. 

3. Apr. 3, 1919. Obs. Mer. Alt. * Aldebaran was 32° 
46' S. Dip 40 ft. 

Required latitude? 

Answer.— Lat. 73° 42' 31" N. 

4. May 4, 1919. Obs. Mer. Alt. * Antares 81° 10' N. 
Index error +3'. Dip 30 ft. 

Required latitude? 

Answer.— Lat. 35° 07' 49" S, 



276 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

5. June 5, 1919. Obs. Mer. Alt. *Regulus 32° 15' N, 
Dip 26 ft. 

Required latitude? 
Answer.— Lat. 45° 29' 56" S. 

6. July 8, 1919. Obs. Mer. Alt. * Fomalhaut 43° 16' S. 
Dip 18 ft. 

Required latitude? 
Answer.— Lat. 16° 46' 29" N. 



TIME OF STAR'S MERIDIAN PASSAGE 

1. Jan. 16, 1919. Find meridian passage *Spica? 
Answer.— Jan. 16d 17h 39'. 

2. Feb. 12, 1919. Find meridian passage * Rigel? 
Answer.— Feb. 12d 7h 44'. 

3. March 20, 1919. Find meridian passage * Antares? 
Answer.— Mar. 20d 16h 34'. 

4. May 19, 1919. Find meridian passage * Sirius? 
Answer.— May 19d 21i 56'. 

5. June 7, 1919. Find meridian passage * Canopus? 
Answer.— June 7d Ih 22'. 

6. Dec. 6, 1919. Find meridian passage * Capella? 
Answer.— Dec. 6d 12h 12'. 

LONGITUDE BY SUN 

1. Jan. 31, 1919, A. M. at ship. Obs. Alt. Sun^s L. L. 
16° 18'. Dip 26 ft. Chron. read 2h 15' P. M., which was 
fast 13' 28". Lat. by D. R. 36° 10' N. 

Required longitude? 

Answer.— Long. 80° 12' 15" W. 

- 2. Feb. 9, 1919, P. M. at ship. Obs. Alt. Sun's L. L. 
18° 30'. Dip 31 ft. Chron. read lOh 15' 28" A. M. which 
was fast 56' 08". Lat. by D. R. 28° 15' S. 

Required longitude? 

Answer.— Longitude 120° 20' 30" E. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 277 

3. Mar. 21, 1919, A. M. at ship. Obs. Alt. Sun's L. L. 
Sr 28'. Dip 26 ft. Chron. read 4h 10' P. M. which was 
slow 28' 10". Lat. by D. R. 18° 16' N. 

Required longitude? 
Answer.— Long. 124° 10' W. 

4. Apr. 3, 1919, A. M. at ship. Obs. Alt. Sun's L. L. 
14° 12'. Dip 32 ft. Chron. read 9h 15' A. M. which was 
slow 46' 10". Lat. by D. R. 41° 08' S. 

Required longitude? 
Answer.— Long. 35° 27' 30" W. 

5. May 6, 1919, P. M. at ship. Obs. Alt. Sun's L. L. 
14° 50'. Dip 29 ft. Chron. read Ih 10' P. M. which was 
slow 43' 12". Lat. by D. R. 18° 28' S. 

Required longitude? 
Answer.— Long. 38° 25' 45" E. 

6. June 3, 1919, A. M. at ship. Obs. Alt. Sun's L. L. 
22° 16'. Dip 28 ft. Chron. read Ih 48' 12" P. M. which 
was slow Ih 18' 08". Lat. by D. R. 27° 30' N. 

Required longitude? 
Answer.— Long. 122° 34' W. 

NOON POSITION SIGHTS 

1. July 10, 1919, A. M. at ship. Obs. Alt. Sun's L. L. 
20° 15'. Dip 20 ft. Chron. read 9h 15' 28" A. M. which 
was slow on June 8th 40' 10" and losing 1".9 daily. Lat. at 
noon was 28° 16' N. Ship ran from sight to noon S 28° W 
(true) 46 miles. 

Required ship's position at sight and noon? 

Answer.— Lat. at sight 28° 56' 36" N. Long, at sight 
46° 11' 15" W. Lat. at noon 28° 16' 00" N. Long, at noon 
46° 36' W. 

2. Aug. 10, 1919, P. M, at ship. Obs. Alt. Sun's L. L. 
19° 15'. Dip 26 ft. Chron. read 9h 16' 18" A. M. which 
was slow on July 8th, 30' 12" and losing 4". 7 daily. Lat. 
at noon was 14° 18' S. Ship ran from noon to sight N 51° W 
(true) 38 miles. 

Required ship's position at sight and noon? 
Answer.— Sight: Lat. 13° 54' 06" S, Long. 98° 52' 45" E. 
Noon Lat. 14° 18' 00" S, Long. 99° 23' 15" E. 



278 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

3. Sept. 23, 1919, A. M. at ship. Obs. Alt. Sun^s L. L. 
24° 10'. Dip 38 ft. Chron. read 2h 16' 28'' P. M. which 
was fast on Aug. 16th 3' 10" and losing 3 ".5 daily. Lat. at 
noon was 41° 10' N. Ship ran from sight to noon S 32° E 
(true) 53 miles. 

Required ship's position at sight and noon? 
Answer.— Sight : Lat. 41° 54' 54" N, Long. 92° 21' 30" W 
Noon: Lat. 41° 10' 00" N, Long. 91° 43' 30" W 

4. Oct. 7, 1919, A. M. at ship. Obs. Alt. Sun's L. L. 
28° 10'. Dip 33 ft. Chron. read 6h 15' 20" A. M. which 
was slow on Sept. 22d 4' 10" and gaining 9".5 daily. Lat. 
at noon was 36° 42' S. Ship ran from sight to noon S 48° 
E (true) 39 miles. 

Required ship's position at sight and noon? 
Answer.— Sight: Lat. 36° 15' 54" S, Long. 24° 25' 45" E. 
Noon: Lat. 36° 42' 00" S, Long. 25° 01' 45" E. 

5. Nov. 14, 1919, P. M. at ship. Obs. Alt. Sun^s L. L. 
23° 10'. Dip 26 ft. Chron. read 9h 58' 10" which was slow 
on Oct. 8th 5' 40" and losing 6".4 daily. Long, by D. R. 
110° W. Lat. at noon was 31° 15' N. Ship ran from 
noon to sight N 22° E (true) 43 miles. Required ship's 
position at sight and noon? 

Answer.— Sight: Lat. 31° 54' 54" N, Long. 109° 51' 15"W 
Noon: Lat. 31° 15' 00' N, Long. 110° 10' 15" W 

6. Dec. 3, 1919, A. M. at ship. Obs. Alt. Sun's L. L. 
20° 10'. Dip 25 ft. Chron. read Dec. 2d 18h 15' 28" which 
was slow on Nov. 7th 40' 10" and losing 3".8 daily. Lat. 
at noon was 31° 48' N. Ship ran from sight to noon S 40° 
E (true) 46 miles. 

Required ship's position at sight and noon? 
Answer.— Sight: Lat. 32° 23' 12" N, Long. 27° 25' E. 
Noon: Lat. 31° 48' 00" N, Long. 28° 00' E. 



DEVD^TION BY AZIMUTH 

1. Jan. 11, 1919, A. M. at ship. Chron. read llh 10' 
A. M. Lat. 16° 18' N, Long. 56° 28' W. Sun bore by com- 
pass N 123° E. Variation 8° W. 

Required error and deviation of compass? 

Answer. — Error of compass 6° W. Deviation 2° E. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 279 

2. Mar. 21, 1919, A. M. at ship. Chron. read 4h 10' 
P. M. Lat. 28° S, Long. 140° 10' W. Sun bore by compass 
S 110° E. Variation 8° E. 

Required error and deviation of compass? 

Answer. — Error of compass 15° E. Deviation 7° E. 

3. May 3, 1919, P. M. at ship. Chron. read 8h 15' 
A. M. Lat 46° N, Long. 110° 12' E. Sun bore by compass 
N 110° W. Variation 6° W. 

Required error and deviation of compass? 

Answer. — Error of compass 5° E. Deviation 11° E. 

4. July 4, 1919, P. M. at ship. Chron. read lOh 20' 
P. M. Lat. 24° S, Long. 93° 10' W. Sun bore by compass 
S 118° 30' W. Variation 8° E. 

Required error and deviation of compass? 

Answer. — Error of compass 5° 25' E. Deviation 2° 
35' W. 

5. Sept. 3, 1919, A. M. at ship. Chron, read 4h 08' 
A. M. Lat. 40° N, Long. 55° 50' E. Sun bore by compass 
N 110° E, Variation 8° W. 

Answer. — Error of compass 8° W. Deviation 0°. 

6. Nov. 8, 1919, A. M. at ship. Chron. read Ih 12' 16" 
P. M. Lat. 28° N, Long. 100° W. Sun bore by compass 
N 112° E. Variation 4° E. 

Required error and deviation of compass T 

Answer. — Error of compass 2° W. Deviation 6° W. 



DEVLA.TION BY AMPLITUDE 

1. Feb. 7, 1919. Sun bore at setting S 80° W. Chron. 
read 6h 16' P. M. Lat. 28° 10' N. Variation 9° W. 

Required error and deviation of compass? 

Answer. — Error of compass 7° 36' W. Deviation V 
24' E. 

2. Mar. 21, 1919. Sun bore at rising N 81° E. Chron. 
read lOh 10' A. M. Lat. 18° 48' S. Variation 4° E. 

Required error and deviation of compass? 

Answer.— Error of compass 9° E. Deviation 5"^ E. 



280 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

3. July 4, 1919. Sun bore at setting N 81° W. Chron. 
read 8h 10' P. M. Lat. 0° 10' S. Variation 10° E. 

Required error and deviation of compass? 
Answer. — Error of compass 13® 56' E. Deviation 3° 
56' E. 

4. Oct. 7, 1919. Sun bore at rising N 89° E. Chron. 
read 8h 10' A. M. Lat. 46° 06' N. Variation 10° E. 

Required error and deviation of compass? 
Ansv/er. — Error of compass 8° 25' E. Deviation V 
35' W. 

5. November 30, 1919. Sun bore at setting S 69° W. 
Chron. read lOh 16' P. M. ^ Lat. 32° 10' S. Variation 2° E. 

Required error and deviation of compass? 
Answer, — Error of compass 4° 47' W. Deviation 6° 
47' W. 

6. Dec. 3, 1919. Sun bore at rising S 60° E. Chron. 
read 5h 06' P. M. Lat. 38° 16' N. Variation 7° W. 

Required error and deviation of compass? 
Answer. — Error of compass 1° 27' W. Deviation 5° 
33' E. 



LATITUDE BY POLARIS 

1. Sept. 18, 1919, P. M. at ship. Obs. Alt. *Polaris 
16° 15'. Dip 27 ft. Chron. read llh 57' 18" P. M., slow 
8' 12" Long, 113° 26' W. 

Required latitude? 

Answer.— Latitude 16° 57' 17" N. 

2. Mar. 12, 1919, A. M. at ship. Obs. Alt. * Polaris 
23° 16'. Dip 16 ft. Chron. read Ih 12' 13" A. M. Long. 
25° 20' E. 

Required latitude? 

Answer.— Latitude 24° 16' 19" N. 

3. Feb. 8, 1919, A. M. at ship. Obs. Alt. *Polaris 
28° 14'. Dip 26 ft. Chron. read Ih 16' P. M. Long. 
98° 16' W. 

Required latitude? 

Answer.— Latitude 29° 02' 23" N. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 281 

4. July 6, 1919, P. M. at ship. Obs. Alt. * Polaris 14^ 
20'. Dip 30 ft. Chron. read Ih 48' P. M. Long. 74° 10' E. 

Required latitude? 

Answer.— Latitude 15° 18' 10" N. 

5. June 6, 1919, A. M. at ship. Obs. Alt. * Polaris 
38° 20'. Dip 26 ft. Chron. read llh 16' 20" A. M. Long. 
85° 50' W. 

Required latitude? 

Answer.— Latitude 37° 27' 17" N. 

6. Dec. 7, 1919, P. M. at ship. Obs. Alt. * Polaris 42"^ 
06'. Dip 40 ft. Chron. read 8h 16' A. M. Long. 160° 
45' E. 

Required latitude? 

Answer.— Latitude 40° 56' 56" N. 



ALTITUDE AZIMUTH. LONGITUDE BY SUN AND MER-= 
CATOR'S SAILING COMBINED 

1. June 20, 1919, A. M. at ship. Obs. Alt. Sun's L. L. 
48° 57' 46". Dip 10 ft. Chron. read 5h 08' 40" A. M. which 
was slow on Feb. 17th 27' 18" and on April 8th was slow 
32' 48". Lat. at noon was 33° 32' 18" N. Ship ran from 
sight to noon N 23° E (true) 35 miles. Sun bore by com- 
pass S 81° 31' E. Variation 1° E. 

Required position of vessel at sight and noon? 

Required error and deviation of compass by altitude 
azimuth, and true course and distance by Mercator's sailing 
from noon to Lat. 48° 10' N, Long. 40° E? 

Ansv/er.— Sight : Lat. 33° 00' 06" N. Long. 47° 27' 30" E. 
Noon: Lat. 33° 32' 18" N, Long. 47° 44' 00" E. Error of 
compass 6° 59' W. Deviation 7° 59' W. True course 
N 21° 44' W. Distance 945.2 miles. 

2. Jan. 31, 1919, A. M. at ship. Obs. Alt. Sun's L. L. 
17° 40'. Index error +3' 00". Dip 16 ft. Chron. read 
Jan. 31st 4h 40' 15" which was slow on Oct. 31st 31' 20" 
and on Dec. 10th was slow 32' 40". Lat. at noon was 
35° 59' N. Ship ran from sight to noon S 67° W (true) 26 
miles. Sun bore by compass East. Variation 22° 15' E. 

Required position of vessel at sight and noon ; error and 
deviation of compass by altitude azimuth, and true course 



282 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

and distance from noon to Lat. 25° 50' N, Long. 100° W. 
by Mercator's sailing? 

Answer.— Sight: Lat. 36° 09' 12" N, Long, 126° 16' 
15" W. Noon: Lat. 35° 59' 00" N, Long. 126° 45' 45" W. 
Error of compass 38° 52' E. Deviation 16° 37' E. True 
course S 66° 13' E. Distance 1510 miles. 

3. Aug. 10, 1919, A. M. at ship. Obs. Alt. Sun's L. L. 
16° 05' 30". Dip 11 ft. Chron. read 5h 17' 26" A. M. 
which was slow on March 17th 4' 25" and on June 9th was 
fast 6' 53". Lat. at noon was 47° 25' N. Ship ran from 
sight to noon S 50° W (true) 40 miles. Sun bore by com- 
pass East. Variation 4° 30' E. 

Required position of vessel at sight and noon? 

Required error and deviation of compass by altitude 
azimuth, and true course and distance by Mercator's sailing 
from noon to Lat. 25° 10' N, Long. 10° 06' E? 

Answer.— Sight: Lat. 47° 50' 42" N, Long. 22° 37' 45" E. 
Noon: Lat. 47° 25' 00" N, Long. 21° 51' 45" E. Error of 
compass 5° 54' W. Deviation 10° 24' W. True course 
S 22° 54' W. Distance 1449 miles. 

4. Mar. 21, 1919, A. M. at ship. Obs. Alt. Sun's L. L. 
29° 41'. Dip 12 ft. Chron. read 4h 19' 27" P. M. which 
was fast on Jan. 18th 43' 43" and losing 10".7 daily. Lat. 
at noon was 38° 20' S. Ship ran from sight to noon 
North (true) 20 miles. Sun bore by compass S 79° E. 
Variation 35° W. 

Required position of vessel at sight and noon; error and 
deviation of compass by altitude azimuth and true course 
and distance by Mercator's sailing from noon to Lat. 10° 
08' S, Long. 178° E. 

Answer.— Sight: Lat. 38^ 40' S, Long. 105° 12' 30" W. 
Noon: Lat. 38° 20' S, Long. 105° 12' 30" W. Error of 
compass 38° 20' W. Deviation 3° 20' W. True course 
N 67° 53' W. Distance 4494 miles. 

5. Sept. 24, 1919, P. M. at ship. Obs. Alt. Sun's L. L. 
21° 10'. Dip 12 ft. Chron. read Ih 10' 10" P. M. which 
was fast on June 1st 28' 2" and on August 1st was fast 29' 
37". Lat. at noon was 16° 00' S. Ship ran from noon 
to sight N 36° W (true) 42 miles. Sun bore by compass 
S 80° W. Variation 18° 30' E. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 283 

Required ship's position at sight and noon; error and 
deviation of compass by altitude azimuth and true course 
and distance by Mercator's saiHng from noon to Lat. 8"^ 
14' N. Long. 3° 10' W. 

Answer.— Sight: Lat. 15° 26' S. Long. 56° 10' 15" E. 
Noon: Lat. 16° 00' S, Long. 56° 36' 00" E. Error of com- 
pass 16° E. Deviation 2° 30' W. True course N 67° 52' 
W. Distance 3859 miles. 

6. Nov. 8, 1919, A. M. at ship. Obs.~Alt. Sun's L. L. 
42° 00'. Dip 13 ft. Chron. read 2h 40' 22" P. M. which 
was fast on Sept. 24th Ih 12' 56" and losing 3".6 daily. 
Lat. at noon was 50° 02' S. Ship run from sight to noon 
N 28° E (true) 38 miles. Sun bore by compass N 70° 30' 
E. Variation 14° 18' W. 

Required position of ship at sight and noon; error and 
deviation of compass by altitude azimuth and true course 
and distance by Mercator's sailing from noon to Lat. 25° 
00' S, Long. 30° W. 

Answer.— Sight: Lat. 50° 35' 36" S, Long. 68° 24' 30" W. 
Noon: Lat. 50° 02' 00" S, Long. 67° 56' 45" W. Error of 
compass 10° 46' W. Deviation 3° 32' E. True course 
N 49° 52' E. Distance 2330 miles. 

LATITUDE BY PLANET 

1. June 12, 1919. Obs. Mer. Alt. Planet Mars 47° 18' N. 
Dip 26 ft. Chron. read 4h 22' P. M. 

Required latitude? 
Answer.— Lat. 20° 12' 20" S. 

2. July 6, 1919. Obs. Mer. Alt. Planet Saturn 38° 28' 
N. Dip 30 ft. Chron. read 5h 38' P. M. 

Required latitude? 
Answer.— Lat. 37° 22' 29" S. 

3. Feb. 8, 1919. Obs. Mer. Alt. Planet Venus 48° 41' S, 
Dip 28 ft. Chron. read 3h 40' P. M. 

Required latitude? 
Answer.— Lat. 31° 07' 55" N. 

4. April 15, 1919. Obs. Mer. Alt. Planet Jupiter 58° 
10' S. Dip 26 ft. Chron. read Ih 14' A. M. 

Required latitude? 
Answer.— Lat. 55° 18' 27" N. 



284 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



LATITUDE BY EX-MERIDIAN ALTITUDE OF SUN 

1. Jan. 30, 1919. Ex-Mer. Alt. Sun's L. L. 47° 48' S. 
Dip 26 ft. Chron. read 7h 40' 18''. Long. 108° 30' W, 
Lat. D. R. 24° N. 

Required latitude at sight? 
Answer.— Lat. 24° 07' 46" N. 

2. Mar. 21, 1919. Ex-Mer. Alt. Sun's L. L. 72° 10' N. 
Dip 30 ft. Chron. read 7h 50' 30" A. M. Long. 61° 15' E, 
Lat. by D. R. 18° S. 

Required latitude at sight? 
Answer.— Lat. 17° 33' 33" S. 

3. July 12, 1919. Ex-Mer. Alt. Sun's L. L. 58° 16' S. 
Dip 30 ft. Chron. read 5h 50' 12" P. M. Long. 90° W, 
Lat. by D. R. 53° 40' N. 

Required latitude at sight? 
Answer.— Lat. 53° 30' 13" N. 

4. Apr. 18, 1919. Ex-Mer. Alt. Sun's L. L. 54° 28' N. 
Dip 26 ft. Chron. read 3h 48' 32". Long. 124° E, Lat. 
byD. R.25°S. 

Required latitude at sight? 
Answer.— Lat. 24° 54' 28" S. 

5. Dec. 25, 1919. Ex-Mer. Alt. Sun's L. L. 64° 20' N. 
Dip 26 ft. Chron. read 2h 10' P. M. Long. 31° W, Lat. 
by D. R. 49° S. 

Required latitude at sight? 
" Answer.— Lat. 48° 52' 40" S. 

6. Oct. 16, 1919. Ex-Mer. Alt. Sun's L. L. 79° 20' S. 
Dip 28 ft. Chron. read 2h 01' A. M. Long. 149° 10' E, 
Lat. D. R. 2° N. 

Required latitude at sight? 
Answer.— Lat. 1° 35' 39" N. 

LONGITUDE BY FIXED STAR AND PLANET 

1. Apr. 9, 1919, P. M. at ship. Obs. Alt. *Sirius 28° 
41', bearing West. Dip 26 ft. Chron. read 5h 09' 40" 
P. M. which was fast 28' 10", Lat. 23° 40' N, Long, by 
D. R. 60° E. 

Required longitude? 

Answer.— Long. 60° 39' E. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 285 

2. Feb. 9, 1919, A. M. at ship. Obs. Alt. *Arcturus 
36° 20', bearing East. Dip 28 ft. Chron. read lOh 28' 
10'' A. M. Lat. 42° 10' N, Long, by D. R. 141° W. 

Required longitude? 

Answer.— Long. 140° 55' 15" W, 

3. Feb. 13, 1919, A. M. at ship. Obs. Alt. *Procyon 
30° 00', bearing West. Dip 36 ft. Chron. read Feb. 12th 
16h 40' 28" which was slow of G. M. T. 3' 26". Lat. 28° 
50' N, Long, by D. R. 41° W. 

Required longitude? 
Answer.— Long. 40° 37' 15" W. 

4. May 19, 1919, P. M. at ship. Obs. Alt. *Spica 32° 
46', bearing East. Dip 36 ft. Chron. read Ih 28' P. M. 
Lat. 38° 20' S, Long, by D. R. 65° E. 

Required longitude? 
Answer.— Long. 65° 26' 15" E. 

5. Jan. 29, 1919, A. M. at ship. Obs. Alt. Planet 
Venus 26° 10', bearing East. Dip 26 ft. Chron. read Ih 
13' P. M. Lat. 28° 28' N, Long, by D. R. 47° W. 

Required longitude? 
Answer.— Long. 47° 23' 15" W. 

6. Oct. 6, 1919, A. M. at ship. Obs. Alt. Planet Saturn 
20° 14' bearing East. Dip 30 ft. Chron. read Oh 36' A. M. 
Lat. 38° 12' N, Long, by D. R. 64° E. 

Required longitude?. 
Answer.— Long. 63° 49' E. 



LATITUDE BY MOON 

1. Apr. 21, 1919. Obs. Mer. Alt. Moon's L. L. 38° 16', 
bearing North. Dip 26 ft. Chron. read Ih 42' A. M. 

Required latitude? 
Answer.— Lat. 71° 50' 19" S. 

2. Aug. 16, 1919. Obs. Mer. Alt. Moon's L. L. 46° 26', 
bearing South. Dip 30 ft. Chron. read Ih 36' P. M. 

Required latitude? 
Answer.— Lat. 55° 05' 39" N. 



286 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

3. Sept. 15, 1919. Obs. Mer. Alt. Moon's L. L. 78° 28', 
bearing North. Dip 26 ft. Chron. read 6h 28' A. M. 

Required latitude? 
Answer.— Lat. 8° 44' 32" N. 

4. June 13, 1919. Obs. Mer. Alt. Moon's L. L. bS"" 14' 
S. Dip 32 ft. Chron. read 4h 09' P. M. 

Required latitude? 
Answer.— Lat. 14° 30' N. 

5. Nov. 25, 1919. Obs. Mer. Alt. Moon's L. L. 70° 14', 
bearing North. Dip 26 ft. Chron. read 7h 08' P. M. 

Required latitude? 
Answer.— Lat. 39° 03' 28" S. 

6. Dec. 5, 1919. Obs. Mer. Alt. Moon's L. L. 68° 14' 
bearing South. Dip 26 ft. Chron. read Dec. 5th 12h 43'. 

Required latitude? 
Answer.— Lat. 39° 54' 44" N. 



LONGITUDE BY SUNRISE AND SUNSET OBSERVATIONS 

1. Dec. 2, 1919. Sun's L. L. at Sunrise. Chron. read 
7h 10' which was slow 45' 10". Lat. 28° 14' N, Long, by 
D. R. 19° 40' W. 

Required longitude? 
Answer.— Long. 19° 31' 45" W. 

2. Mar. 21, 1919. Sun's U. L. at Sunset. Chron. 
read 5h 10' which was slow 30' 00". Lat. 14° 16' S, Long. 
by D. R. 8° E. 

Required longitude? 
Answer.— Long. 7° 46' E. 

3. May 6, 1919. Sun's L. L. at Sunrise. Chron. read 
Oh 16' which was slow 58' 00", Lat. 34° 06' S, Long, by D. R. 
98° 10' W. 

Required longitude? 
Answer.— Long. 98° 21' 45" W. 

4. Jan. 2, 1919. Sun's U. L. at Sunrise. Chron. read 
Ih 15' 20", which was slow 41' 28". Lat. 36° 12' N, Long, 
by D. R. 78° 45' E. 

Required longitude? 
Answer.— Long. 78° 34' 15" E. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 287 

5. October 11, 1919. Sun's U. L. at Sunset. Chron. 
read Ih 50' which was slow 8' 10". Lat. 43° 16' S, Long, 
by D. R. 65° E. 

Required longitude? 
Answer.— Long. 64° 50' E. 

6. July 10, 1919. Sun's L. L. at Sunset. Chron. read 
lOh 05' (correct) Lat. 13° 14' N, Long, by D. R. 126° E. 

Required longitude? 
Answer.— Long. 125° 57' 15" E. 

TIME OF HIGH AND LOW WATER 

1. Jan. 28, 1919. Find time of high and low water in 
A. M. and P. M. at Antwerp, Belgium? 

Answer.— High water 12h 54' A. M., Ih 21' P. M. 
Low water 7h 06' A. M., 7h 33' P. M. 

2. July 4, 1919. Find time of high and low water A. M. 
and P. M. at Guaymas, Mexico? 

Answer.— High water 4h 32' A. M., 4h 54' P. M. 
Low water lOh 50' A. M., llh 12' P. M. 

3. Mar. 10, 1919. Find time of high and low water 
A. M. and P. M. at Copenhagen, Denmark? 

Answer.— High water 4h 09' A. M., 4h 37' P. M. 
Low water lOh 25' A. M., lOh 53' P. M. 

4. Sept 12, 1919. Find time of high and low water A. M. 
and P. M. at Castillos, Uruguay? 

Answer.— High water 9h 53' A. M., lOh 20' P. M. 
Low water 3h 41' A. M., 4h 08' P. M. 

5. June 16, 1919. Find time of high and low water 
A. M. and P. M. at Alligator Reef, Florida? 

Answer.— High water lOh 28' A. M., lOh 52' P. M. 
Low water 4h 06' A. M., 4h 30' P. M. 

6. May 3, 1919. Find time of high and low water A. M, 
and P. M. at Cape Wilberforce, AustraHa? 

Answer.— High water lOh 23' A. M., lOh 54' P. M. 
Low water 4h 11' A. M., 4h 42' P. M. 



288 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

EXPLANATION OF ILLUSTRATIONS SHOWING METHOD 
OF PLOTTING ONE OBSERVATION OF SUN OR STAR 
ON A MERCATOR CHART 

This method is the most practical and simple that can be used on 
board of a ship, and is strongly recommended to the student of navigation. 

The idea of the method is to find the longitude when an error in 
latitude has been made at the time of observation. 

When the sun is on the prime vertical an error in latitude wdll have 
no effect on the longitude as the sun's bearing will then be true East or 
West, and the line of bearing at right angles to this or 90° away, will 
be North and South. At all other times an error in latitude used in an 
example for longitude, will make a difference in the longitude found. 

To lay off on chart proceed as follows: 

Take observation of sun or star, using the latitude by D. R. to work 
the observation with. 

After obtaining this position, place it on the chart. 

Enter azimuth table and take out true bearing of body observed, 
using local apparent time for sun, hour angle for star. 

Draw a line through the position already placed on chart at right 
angles to true bearing or 90° from it. 

This will give the line of bearing, and the ship will be on this line 
somewhere if no error in latitude has been made. 

Now when we obtain the latitude at noon, knowing the course and 
distance the ship has sailed between sight and noon, v/e find the correct 
latitude we were in at time of observation by working the latitude back 
to sight, using the difference of latitude obtained from Table 2 for the 
course and distance. 

We then take a pair of dividers and obtain the length of the correct 
latitude at time of observation on the side of the chart. 

Where the dividers meet the line of bearing, keeping one point of 
dividers on parallel of latitude used, will be the ship's correct position 
at time of sight. 

Allowing the difference of longitude found from course and distance 
between sight and noon, to the longitude found on line of bearing, will 
give the ship's noon position. 

This method avoids the working of the sight over again, after the 
correct latitude has been found. 

The following examples will illustrate the change in longitude for 
an error in latitude. 

By taking a pair of dividers on the line in Lat. 50° 40' N, the longi- 
tude will be found to be 166° 37' E. 

In Lat. 50° 20' N, the longitude will be 166° 13' 30" E. 

This will illustrate the amount an error in latitude will affect the 
longitude on this bearing, and also the method of obtaining the longi- 
tude at time of observation with correct latitude. 









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- 






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To lace page t89. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 289 



EXPLANATION OF ILLUSTRATION SHOWING METHOD OF 
PLOTTING POSITION LINES ON MERCATOR CHART 
BY MARCQ ST. HILAIRE METHOD 

The dead reckoning position for first observation is placed 
on chart. 

A Hne representing the body's true bearing is drawn 
through this dead reckoning position. 

The altitude difference is measured from this position 
towards or away from the body. 

In this illustration the altitude difference is —5' 45^'. 
Or 5J miles on line of bearing away from the body. As the 
sun was in the East in A. M., this would be allowed to the 
westward. 

The first hne of bearing is drawn at right angles or 90°, to 
this bearing. 

The course and distance is allowed between observations 
same as in Sumners Method, and a line drawn parallel to 
first line on this course and distance. 

The second dead reckoning position is then placed on 
chart, and a line representing the true bearing drawn through 
it. 

In this case the altitude difference is + 4' 40'', which 
means toward the body on the line of bearing. 

The second line is then drawn at right angles to true 
bearing through this position, and where the second line 
crosses the projection of first line will be ship's position at 
second observation. 



200 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



EXPLANATION OF ILLUSTRATION SHOWING METHOD OF 
PLOTTING SUMNER LINES ON MERCATOR CHART 

The first line of bearing is the Hne drawn between the two 
positions found by first altitude, and is at right angles to 
sun's true bearing. 

Example: Sun's true bearing N 130° 30' E-90° equals 
N 40° 30' E, which is the angle of the first line. 

Course N 56° W (true) distance 46 miles is the line drawn 
allowing for the course and distance run between first and 
second observations. 

The first line of bearing projected is the line drawn par- 
allel to first line of bearing allowing for the course and dis- 
tance. 

Second line of bearing is the line drawn between the two 
positions found by second altitude, and is at right angles to 
sun's true bearing. 

Example: Sun's true bearing N 146° E-90° equals N 
56° E which is the angle of second line. 

Where the second line crosses the projection of first Hne 
will be ships position at second observation. 




-^^*/^. 



4IT. 



-f^*//'. 



-#r*>^- 






r« /MM |NV« «M' 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 291 



EXTRACTS FROM THE AMERICAN NAU-^tcAL ALMANAC 
FOR THE YEAR 1919 

RIGHT ASCENSION OF THE MEAN SUN 
AT GREENWICH MEAN NOON 





JANUARY, 


1919 




JULY, 1919 


Day Right Ascension 


Day Right Ascension 


28 


20h 26' 


48". 1 


2 


6h 37' 


54". 1 


29 


20h 30' 


44". 7 


3 


6h 41' 


50". 6 


30 


20h 34' 


41". 2 


4 


6h 45' 


47". 2 


31 


20h 38' 


37". 8 


6 


6h 49' 


43". 8 








6 


6h 53' 


40". 3 


FEBRUARY, 


1919 


7 


6h 57' 


36". 9 


1 


20h 42' 


34". 3 


14 


7h 25' 


12". 8 


7 


21h 06' 


13". 7 


15 


7h 29' 


9". 3 


8 


21h 10' 


10". 2 


16 


7h 33' 


5". 9 


9 


21h 14' 


6". 8 








10 


21h 18' 


3". 3 




AUGUST, 1919 


11 


21h 21' 


59". 9 


4 


8h 48' 


0".4 


12 


21h 25' 


56". 4 


6 


8h 51' 


57". 


13 


21h 29' 


53". 


6 


8h 55' 


53". 6 


17 


21h 45' 


39". 2 








18 


21h 49' 


35". 8 


SEPTEMBER, 


1919 


19 


21h 53' 


32". 3 


17 


Dh 41' 


28". 8 


20 


21h 57' 


28". 9 


18 


llh 45' 


25". 4 








19 


llh 49' 


21". 9 




MARCH, 1919 








10 


23h 8' 


26". 8 


( 


OCTOBER, 1919 


11 


23h 12' 


23". 4 


4 


12h 48' 


30". 2 


12 


23h 16' 


19". 9 


5 


12h 52' 


26". 7 








6 


12h 56' 


23". 3 




APRIL, 1919 


24 


14h 7' 


21". 2 


7 


Oh 58' 


50". 3 


25 


14h 11' 


17". 8 


8 


Ih 2' 


46". 8 


26 


14h 15' 


14". 4 


9 


Ih 6' 


43". 4 








lOj 


Ih 10' 


40". 


NOVEMBER, 


1919 








8 


15h 6' 


29". 6 




MAY, 1919 


9 


15h 10' 


26". 1 


18 


3h 40' 


29". 


10 


15h 14' 


22". 7 


19 


3h 44' 


25". 6 








20 


3h 48' 


22". 1 


DECEMBER, 


1919 


21 


3h 52' 


18". 7 


5 


16h 52' 


56". 6 








6 


16h 56' 


53". 1 




JUNE, 1919 


7 


17h 0' 


49". 7 


4 


4h 47' 


30". 5 








5 


4h 51' 


27". 








6 


4h 55' 


23". 6 








7 


4h 59' 


20". 2 








8 


6h 3' 


16",7 









292 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



THE SUN 



JANUARY, 1919 





WEDNESDAY 


, 1 




THURSDAY, 


30 


G. M. T. Sun's 


Equation 


G. M. T. Sun's 


Equation 


Hrs. 


Declination 


of Time 


Hrs, 


Declination 


of Time 


4 


-23° 3'. 4 


-3' 23". 9 





-17° 52'. 


-13' 18". 9 


6 


23° 3'.0 


3' 26". 3 


2 


17° 50'. 6 


13' 19". 8 


8 


23° 2'. 6 


3' 28". 6 


4 


17° 49'. 3 


13' 20". 6 


10 


23° 2'. 2 


3' 31". 


6 


17° 47'. 9 


13' 21". 5 


12 


23° 1'.8 


3' 33". 4 


8 


17° 46'. 5 


13' 22". 3 


14 


23° 1'.4 


3' 35". 8 


10 


17° 45'. 2 


13' 23". 2 


16 


23° I'.O 


3' 38". 2 


12 


17° 43'. 8 


13' 24". 


18 


23° 0'.6 


3' 40". 5 


14 


17° 42'. 4 


13' 24". 8 


20 


23° O'.l 


3' 42". 9 


16 


17° 41'. 1 


13' 25". 6 


22 


22° 59'. 7 


3' 45". 3 


18 


17° 39'. 7 


13' 26". 4 


H. D. 


0'.2 


1".2 


20 


17° 38'. 3 


13' 27". 3 








22 


17° 37'. 


13' 28".l 




THURSDAY, 


2 


H. D. 


0'.7 


0".4 





-22° 59'. 3 


-3' 47". 6 








2 


22° 58'. 9 


3' 50". 




FRIDAY, 31 


H. D. 


0'.2 


1".2 





- 17° 35'. 6 


-13' 28". 9 








2 


17° 34'. 2 


13' 29". 6 




FRIDAY, 10 




4 


17° 32'. 8 


13' 30". 4 


22 


-21° 56'. 2 


-7' 43". 5 


6 


17° 31'. 4 


13' 31". 2 


H. D 


0'.4 


1".0 


8 


17° 30'. 


13' 32". 








10 


17° 28'. 7 


13' 32". 7 




SATURDAY, ] 


LI 


12 


17° 27'. 3 


13' 33". 5 





-21° 55'. 5 


-7' 45". 5 


14 


17° 25'. 9 


13' 34". 3 


2 


21° 54'. 7 


7' 47". 5 


16 


17° 24'. 5 


13' 35". 


H. D. 


0'.4 


1".0 


18 


17° 23'. 1 


13' 35". 7 




FRIDAY, 24 




20 


17° 21'. 7 


13' 36". 5 


8 


-19° 18'. 6 - 


-12' 7". 5 


22 


- 17° 20'. 3 


-13' 37". 2 


10 


19° 17'. 4 


12' 8". 8 


H. D. 


0'.7 


0".4 


12 


19° 16'. 2 


12' 10". 








H. D. 


0'.6 


0".6 
















SEMI-DIAMETER 








Jan. 


1 
11 
21 
31 


16'. 30 
16'. 29 
16'. 28 
16'. 26 



Note : The equation of time is to be applied to the G. M. T. in accordance 
with the sign as given. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 293 



FEBRUARY, 1919 





SATURDAY, 


1 




TUESDAY, 18 


G. M. T 


Sun's 


Equation 


G. M. T. 


Sun's Equation 


Hrs. 


Declination 


of Time 


Hrs. 


Declination of Time 


16 


-17° 7'.6- 


-13' 43". 6 


6 


-11° 48'. 7 -14' 7". 2 


18 


17° 6M 


13' 44". 3 


8 


11° 46'. 9 14' 6". 8 


20 


17° 4'. 7 


13' 44". 9 


10 


11° 45'. 2 14' 6". 4 


H.D. 


0'.7 
FRIDAY, 7 


0".3 


H.D. 


0'.9 0".2 
SUNDAY, 23 


4 


15° 29'. 4 ■ 


-14' 15". 8 


10 


-9° 57'. 4 -13' 33"-4 


6 


15 27 .9 


14 16 .1 


12 


9 55 6 13 32 .7 


8 


15 26 .3 


14 16 .4 


14 


9 53 .7 13 32 .0 


H.D. 


0.8 
SATURDAY 


.1 

, 8 


H.D. 


0.9 .3 


18 


-14° 59'. 6 - 


-14' 20". 5 






20 


14° 58M 


14' 20". 7 




SEMI-DIAMETER 


22 


14° 56'. 5 


14' 20". 8 


Feb. 


1 16'. 26 


H.D. 


0'.8 


0".l 




11 16'. 23 
21 16'. 20 




SUNDAY, 9 


1 


March 3 16'. 16 





-14° 54'. 9 - 


-14' 21" 






2 


14° 53'. 3 


14' 21". 2 






4 


14° 51'. 7 


14' 21". 4 






6 


14° 50'. 1 


14' 21". 5 






8 


14° 48'. 5 


14' 21". 7 






10 


14° 46'. 9 


14' 21". 8 






H.D. 


0'.8 


0".l 
MARCH. 


1919 






MONDAY, 10 


' 


THURSDAY, 13 


G. M. T. 


Sun's 


Equation 


G. M. T. 


Sun's Equation 
Declination of Time 


Hrs. 


Declination 


of Time 


Hrs. 





-4° 24'. 3 - 


-10' 37". 9 


10 


-3° 3'. 9 -9' 43". 4 


2 


4° 22'. 4 


10' 36". 6 


12 


3° 1'.9 9' 42". 


4 


4° 20'. 4 


10' 35". 3 


14 


2° 59'. 9 9' 40". 7 


6 


4° 18'. 4 


10' 34". 


H.D. 


I'.O 0".7 


8 


4° 16'. 5 


10' 32". 7 






10 


4° 14'. 5 


10' 31". 4 


WEDNESDAY, 19 


12 


4° 12'. 6 


10' 30". 1 


14 


-0° 37'. 8 -7' 57". 1 


14 


4° 10'. 6 


10' 28". 8 


16 


0° 35'. 9 7' 55". 7 


16 


4° 8'. 7 


10' 27". 5 


18 


0° 33'. 9 7' 54". 2 


18 


4° 6'. 7 


10' 26". 2 


H.D. 


I'.O 0".7 


20 


4° 4'. 7 


10' 24". 9 






22 


4° 2'. 8 


10' 23". 6 






H.D. 


I'.O 


0".6 




FRIDAY, 21 


THURSDAY, 


20 


G. M. T. 


Sun's Equation 


G. M. T. 


Sun's 


Equation 


Hrs. 


Declination of Time 


Hrs. 


Declination 


of Time 





-0° 4'. 3 -r 31". 8 


4 


-0° 24'. 


-7' 46". 7 


2 


0° 2'. 3 7' 30". 3 


6 


0° 22'. 


7' 45". 2 


4 


-0° 0'.3 7' 28". 7 


8 


0° 20'. 1 


7' 43". 7 


6 


-fO° 1'.7 7' 27". 2 


10 


0° 18'. 1 


7' 42" 2 


8 


0° 3'. 6 7' 25". 7 


12 


0° 16'. 1 


7' 40". 7 


H. D. 


I'.O 0".8 


18 


0° 10'. 2 


7' 36". 3 






20 


0° 8'. 2 


7' 34". 8 


SEMI-DIAMETER 


22 


-0° 6'. 2 


-7' 33". 3 


March 1 16'. 17 


H.D 


I'.O 


0".7 




11 16'. 13 



21 16'. 08 

31 16'. 04 



294 SIMPLE RULES AND PROBLEMS IN NAVIGATION 









APRIL, 


1919 






TUESDAY, 


1 






FRIDAY, 18 


G. M. T 


Sun's 


Equation 


G. M. 


T. Sun's Equation 


Hrs. 


Declination 


of Time 


Hrs. 


Declination of Time 





+4" 14'. 4 


-4' 


11". 3 


12 


+ 10° 43'. 6 +0' 35". 9 


2 


4" 16'. 4 


4' 


9". 8 


14 


10° 45'. 3 0' 37". 


4 


4° 18'. 3 


4' 


8". 3 


16 


10° 47'. 1 0' 38". 2 


H. D. 


I'.O 




0".8 


18 
20 


10° 48'. 8 0' 39". 3 
10° 50'. 6 0' 40". 5 




WEDNESDAY 


\ 2 




22 


10° 52'. 3 0' 41". 6 


20 


,+4° 56'. 9 


-3' 


38". 4 


H. D 


0'.9 0".6 


22 


4° 58'. 8 


3' 


36". 9 






H. D. 


I'.O 




0".7 




TUESDAY, 22 




THURSDAY, 


3 




10 


+ 12° 4'. 3 +1' 26". 8 





+5° 0'.7 


-3' 


35". 4 


12 


12° 6'.0 V 27". 8 


2 


5° 2'. 6 


3' 


33". 9 


14 


12° 7'. 7 1' 28". 8 


4 


5° 4'. 6 


3' 


32". 4 


16 


12° 9'. 4 1' 29". 8 


E. D. 


I'.O 




0".7 


H.D 


0'.8 0".5 




TUESDAY, 


8 






SEMI-DIAMETER 


10 


+7° 4'.1 


-2' 


0".9 




AprH 1 16'. 03 


12 


7° 5'. 9 


1' 


59". 5 




11 15'. 99 


14 


7° 7'. 8 


1' 


58". 1 




21 15'. 94 


H. D. 


0'.9 
THURSDAY, 


17 


0".7 




May 1 15'. 90 


14 


+ 10° 24'. 3 


+0' 


23". 1 






16 


10° 26'. 


0' 


24". 2 






18 


10° 27'. 8 


0' 


25". 4 






20 


10° 29'. 6 


0' 


26". 6 






H. D. 


0'.9 




0".6 
MAY, 


1919 






THURSDAY, 1 






TUESDAY, 6 


G. M. T 


Sun's 


Equation 


G. M. 


T. Sun's Equation 


Hrs. 


Declination 


of Time 


Hrs. 


Declination of Time 





+ 14° 50'. 3 


+2' 


52". 7. 





i-16° 18'. 9 +3' 25". 1 


2 


14° 51'. 8 


2' 


53". 4 


2 


16° 20'. 3 3' 25". 5 


H. D. 


0'.8 




0".3 


4 
6 


16° 21'. 7 3' 25". 9 
16° 23'. 1 3' 26". 4 




FRIDAY, 2 






H.D 


0'.7 0".2 


18 


+15° 22'. 


+3' 


5". 6 






20 


15° 23'. 5 


3' 


6".l 




THURSDAY, 29 


22 


15° 25'. 


3' 


6". 7 





+21° 29'. 8 +2' 55". 5 


H. D. 


0'.7 




0".3 


2 

4 


21° 30'. 6 2' 54". 9 
21° 31'. 4 2' 54". 2 




SATURDAY, 


3 




H.D 


0'.4 0".3 





+ 15° 26'. 5 


+3' 


7". 3 






2 


15° 28'. 


3' 


7". 8 




SEMI-DIAMETER 


4 


15° 29'. 5 


3' 


8". 4 




May 1 15'. 90 


H. D. 


0'.7 




0".3 




11 15'. 86 
21 15'. 83 
31 15'. 80 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 295 







JUNE, 


1919 






TUESDAY, 


3 




SUNDAY, 22 


G. M. T 


Sun's 


Equation 


G. M. T. 


Sun's Equation 
Declination of Time 


Hrs. 


Declination 


of Time 


Hrs. 





H-22^ 13M 


+2' 12". 8 


10 


+23° 26'. 9 -1' 38". 


2 


22° 13'. 7 


2' 12". 


12 


23° 26'. 9 l'39".l 


4 


22° 14'. 3 


2' 11". 2 


14 


23° 26'. 8 r 40". 2 


H.D. 


0'.3 


0".4 


16 
18 


23° 26'. 8 1' 41". 3 
23° 26'. 8 1' 42". 4 




THURSDAY, 


19 


H.D. 


O'.O 0".5 


16 


+23° 25'. 8 


-1' 2". 2 






18 


23° 25'. 9 


1' 3". 2 


SEMI-DIAMETER 


20 


23° 26'. 


1' 4". 3 


June 1 15'. 80 


22 


23° 26'. 


1' 5". 4 




11 15'. 78 ■ 


H.D. 


O'.O 


0".5 




21 15'. 77 







JULY, 


1919 








FRIDAY, 4 






WEDNESDAY, 


9 


G. M. T. 


Sun's 


Equation 
of Time 


G. M. ' 


T. Sun's 


Equation 
of Time 


Hrs. 


Declination 


Hrs. 


Declination 





+22° 57'. 3 


-4' 1".0 


18 


+22° 22'. 5 - 


-4' 58". 6 


2 


22° 56'. 9 


4' 1".9 


20 


22° 21'. 9 


4' 59". 3 


4 


22° 56'. 4 


4' 2". 9 


22 


22° 21'. 3 


5' 0".l 


6 


22° 56'. 


4' 3". 8 


H.D, 


0'.3 


0".4 


8 


22° 55'. 6 


4' 4". 7 








10 


22° 55'. 2 


4' 5". 6 




THURSDAY, 10 


12 


22° 54'. 8 


4' 6". 5 





+22° 20'. 7 - 


-5' 0".8 


14 


22° 54'. 3 


4' 7". 4 


2 


22° 20'. 1 


5' 1".5 


16 


22° 53'. 9 


4' 8". 3 


H. D, 


0'.3 


0".4 


18 


22° 53'. 5 


4' 9". 2 








20 


22° 53'. 


4' 10". 1 




SATURDAY, 12 


22 


22° 52'. 6 


4' 11". 





+22° 5'. 4 - 


-5' 17". 5 


H. D 


0'.2 


0".5 


2 


22° 4'. 8 


5' 18". 2 








4 


22° 4'.1 


5' 18". 8 




SATUEDAY, 


5 


6 


22° 3'. 4 


5' 19". 5 





+22° 62'. 2 


-4' 11". 9 


8 


22° 2'. 7 


5' 20". 1 


2 


22° 51'. 7 


4' 12". 8 


H.D 


0'.3 


0".4 


20 


22° 47'. 6 


4' 20". 7 








22 


22° 47'. 1 


4' 21". 6 




SEMI-DIAMETER 


H.D. 


0'.2 


0".4 




July 1 15' 
11 15' 


.76 
.76 




SUNDAY, 6 






21 15' 


.77 





+22° 46'. 7 


-4' 22". 4 




31 15' 


.79 



2 22° 46'. 2 4' 23". 3 

H.D. 0'.2 0".4 



296 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



AUGUST, 1919 





THURSDAY, 


7 






FRIDAY, 8 






G. M. T 


Sun's 


Equation 


G. M. T 


Sun's 


Equation 


Hrs. 


Decimation 


of Time 


Hrs. 


Declination 


of Time 





+ 16° 39'. 3 


-5' 


43". 8 





+16° 22'. 6 


-5' 


36". 8 


2 


16° 37'. 9 


5' 


43". 3 


2 


16° 21'. 2 


5' 


36". 2 


4 


16° 36'. 6 


5' 


42". 7 


4 


16° 19'. 8 


5' 


35". 6 


6 


16° 35'. 2 


5' 


42". 1 


6 


16° 18'. 4 


5' 


35". 


8 


16° 33'. 8 


5' 


41". 6 


8 


16° 17'. 


5' 


34". 4 


10 


16° 32'. 4 


5' 


41". 


10 


16° 15'. 6 


5' 


33". 7 


12 


16° 31'. 


5' 


40". 4 


H. D. 


0'.7 




0".3 


20 


16° 25'. 4 


5' 


38". 










22 


16° 24'. 


5' 


37". 4 




SATURDAY, 


9 




H. D. 


0'.7 




0".3 


14 


+ 15° 55'. 7 


-5' 


24". 5 










16 


15° 54'. 2 


5' 


23". 8 




SUNDAY, 10 




18 


15° 52'. 8 


5' 


23". 1 





+15° 48'. 5 


-5' 


21". 


20 


15° 51'. 3 


5' 


22". 4 


2 


15° 47'. 


5' 


20". 3 


22 


15° 49'. 9 


5' 


21". 7 


20 


15° 33'. 9 


5' 


13". 8 


H. D. 


0'.7 




0".3 


22 


15° 32'. 5 


5' 


13". 










H. D. 


0'.7 




0".4 




SATURDAY 30 












6 


+9° 12'. 2 


-0' 


45". 5 




MONDAY, 11 




8 


9° 10'. 4 


0' 


44". 





+ 15° 31'. 


-5' 


12". 3 


10 


9° 8'. 7 


0' 


42". 5 


2 


15° 29'. 5 


5' 


11". 5 


H. D. 


0'.9 




0".8 



SEMI-DIAMETER 

August 1 15'. 79 

11 15'. 81 

21 15'. 84 

31 15'. 88 



SEPTEMBER, 1919 



TUESDAY, 2 

G. M. T. Sun's Equation 

Hrs. Declination of Time 

14 +8° O'.O +0' 16". 4 

16 7° 58'. 2 0' 17". 9 

18 7° 56'. 4 0' 19". 5 

H. D. 0'.9 0".8 

WEDNESDAY, 17 

18 +2° 16'. 6 +5' 28". 5 

20 2° 14'. 7 5' 30". 3 

22 2° 12'. 7 5' 32". 

H. D. I'.O 0".9 

TUESDAY, 23 

+0° 14'. 2 +7' 19". 3 

2 0° 12'. 3 7' 21". 

4 0° 10'. 3 7' 22". 8 

6 0" 8'. 4 7' 24". 5 

H. D. I'.O 0".9 



WEDNESDAY, 24 



I M. T. 


Sun's 


Equation 


Hrs. 


Declination 


of Time 





-0° 9'. 2 


+7' 40". 1 


2 


0° 11'. 1 


7' 41". 8 


4 


0° 13M 


7' 43". 6 


H. D. 


I'.O 


0."9 




TUESDAY, ; 


30 


6 


-2° 35'. 4 


+9' 46". 7 


8 


2° 37'. 3 


9' 48". 3 


10 


2° 39'. 3 


9' 50". 


12 


2° 41'. 2 


9' 51". 6 


20 


2° 49'. 


9' 58". 1 


22 


2° 50'. 9 


9' 59". 7 


H. D. 


I'.O 


0".8 



SEMI-DIAMETER 

Sept. 1 15'. 88 

11 15'. 92 

21 15'. 96 

Oct. 1 16'. 01 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 297 



OCTOBER, 1919 



WEDNESDAY, 1 

G. M. T. Sun's Equation 

Hrs. Declination of Time 

-2° 52'. 9 +10' 1".4 

2 2° 54'. 8 10' 3".0 

H. D. I'.O 0".8 

MONDAY, 6 

16 -5° 4'. 3 +11' 46". 7 

18 5° 6'. 3 11' 48". 2 

20 5° 8'. 2 11' 49". 7 

H. D. I'.O 0".7 

SATURDAY, 11 

-6° 43'. 6 +12' 59". 4 

2 6° 45'. 5 13' 0".7 

4 6° 47'. 3 13' 2".0 

H. D. 0'.9 0".6 

WEDNESDAY, 15 



12 


-8° 24'. 8 +14' 5". 3 


14 


8° 26'. 7 14' 6". 4 


16 


8° 28'. 5 14' 7". 5 


18 


8° 30'. 4 14' 8". 6 


[. D. 


0'.9 0".6 




FRIDAY, 17 


8 


-9° 5'. 4 +14' 28". 9 


10 


9" 7'. 3 14' 29". 9 


12 


9° 9'.1 14' 30". 9 


14 


9" 10'. 9 14' 32". 


[. D. 


0'.9 0".5 





SATURDAY, 


18 


G. M. ' 


T. Sun's 


Equation 


Hrs. 


Declination 


of Time 





-9° 20'. 1 +14' 37". 


2 


9° 21'. 9 


14' 38". 


4 


9° 23'. 7 


14' 39". 


H. D 


0'.9 


0".5 




THURSDAY, ; 


23 





-ir 8'.0 +15' 28". 7 


2 


11° 9'. 8 


15' 29". 4 


4 


ir 11'. 6 


15' 30". 1 


6 


11° 13'. 3 


15' 30". 8 


8 


11° 15'. 1 


15' 31". 5 


10 


11° 16'. 8 


15' 32". 2 


12 


11° 18'. 6 


15' 32". 9 


14 


11° 20'. 4 


15' 33". 6 


16 


11° 22'. 1 


15' 34". 3 


18 


11° 23'. 9 


15' 35". 


20 


11° 25'. 6 


15' 35". 6 


H. D 


0'.9 


0".3 




SEMI-DIAMETER 


( 


Oct. 1 16 


'.01 




11 16 


'.06 




21 16 


'.10 




31 16 


'.14 



NOVEMBER, 1919 



SATURDAY, 8 

G. M. T. Sun's Equation 

Hrs. Declination of Time 

-16° 21'. 1 +16' 13". 4 

2 16° 22'. 6 16' 13". 1 

4 16° 24'. 1 16' 12". 8 

H.D. 0'.7 0".2 

THURSDAY, 27 

18 -21° 7'. 9 +12' 18". 5 

20 21° 8'. 8 12' 16". 8 

22 21° 9'. 7 12' 15". 2 

H. D. 0'.5 0".8 

FRIDAY, 28 
-21° 10'. 6 +12' 13". 5 
2 21° 11'. 5 12' 11". 8 

H. D. 0'.4 0".8 



FRIDAY, 14 



G. M. T. 


Sun's 


Equation 


Hrs. 


Declination 


of Time 


8 


-18° 7'.1 +15' 33". 1 


10 


18° 8'. 5 


15' 33". 2 


12 


18° 9'. 8 


15' 32". 4 


18 


18° 13'. 7 


15' 30". 1 


20 


18° 15'. 


15' 29". 3 


22 


18° 16'. 3 


15' 28". 5 


H. D. 


0'.7 


0".4 




SUNDAY, 30 


6 


-21° 34'. 1 


+ 11' 26". 9 


8 


21° 34'. 9 


11' 25". 1 


10 


21° 35'. 7 


11' 23". 3 


H. D. 


0'.4 


0".9 



SEMI-DIAMETER 

Nov. 1 16'. 15 

11 16'. 19 

21 16'. 22 

Dec. 1 16'. 25 



298 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



DECEMBER, 1919 





MONDAY, 1 






MONDAY, 15 


G. M. T. Sun's Equation 


G. M. T. 


Sun's 


Equation 
of Time 


Hrs. 


Declination of Time 


Hrs. 


Declination 


18 


-21° 48'. 5 +10' 


53". 9 





-23° 14'. 


+5' 9". 9 


20 


21° 49'. 3 10' 


52". 1 


2 


33° 14'. 3 


5' 7". 5 


22 


21° 50'. 1 10' 


50". 2 


4 


23° 14'. 6 


5' 5".l 


H. D 


0'.4 


0".9 


6 


23° 14'. 9 


5' 2". 7 








8 


23° 15'. 2 


5' 0".3 




TUESDAY, 2 




10 


23° 15'. 4 


4' 57". 9 





-21° 50'. 9 +10' 


48". 3 


12 


23° 15'. 7 


4' 55". 5 


2 


21° 51'. 6 10' 


46". 4 


14 


23° 16'. 


4' 53". 1 


16 


21° 56'. 9 10' 


33". 1 


16 


23° 16'. 2 


4' 50". 7 


18 


21° 57'. 7 10' 


31". 2 


18 


23° 16'. 5 


4' 48". 3 


20 


21° 58'. 4 10' 


29". 3 


20 


23° 16'. 8 


4' 45". 9 


22 


21° 59'. 2 10' 


27". 3 


22 


23° 17'. 


4' 43". 4 


H.D. 


0'.4 


1".0 


H. D. 


O'.l 


1".2 




WEDNESDAY, 3 






TUESDAY, 16 





-21° 59'. 9 +10' 


25". 4 





-23° 17'. 3 + 4' 41". 


2 


22° 0'.6 10' 


23". 5 


2 


23° 17'. 5 


4' 38". 6 


4 


22° r.4 10' 


21". 5 


4 


23° 17'. 8 


4' 36". 2 


6 


22° 2M 10' 


19". 6 


H. D. 


O'.l 


1".2 


H. D. 


0\4 


1".0 









SEMI-DIAMETER 

Dec. 1 16'. 25 

11 16'. 28 

21 16'. 29 

31 16'. 30 



WEDNESDAY, 24 

12 -23° 25'. 8 +0' 28". 

14 23° 25'. 7 0' 25". 5 

16 23° 25'. 6 0' 23". 

H. D. O'.O 1".3 

THURSDAY, 25 

-23° 25'. 3 +0' 13". 

2 23° 25'. 2 0' 10". 5 

4 23° 25'. 1 0' 8".0 

H.D O'.l 1".2 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 299 



APPARENT PLACES OF STARS, 1919— FOR THE UPPER 
TRANSIT OF GREENWICH 



Special Name 
of Star. 



Right Ascension. 



h. m. 



s 



s 



s 



Spica 

Rigel 

Procyon 
Arcturus. . 
Betelgeux. 
Aldebaran . 

Sirius 

Fomalhaut. 
Antares. . . 
Regulus . . . 
Vega 
Capella. . . 



3 57.3 
9 40.8 



6.4 
59.3 
49.6 
18.4 
37.0 
10.7 
27.3 

6.2 
11.2 
45.3 



58.5 
39.8 

5.7 
60.7 
48.7 
17.5 
36.1 
11.1 
29.2 

6.4 
13.0 
44.0 



6 58, 
3 39. 

2 4. 
61, 
3k8, 
2il7. 
5135, 
8112. 
9 30. 



58.3 
39.7 

4.9 
60.8 
48.5 
17.9 
35.3 
13.9 
30.6 

5.3 
15.2 
44.0 



57.7 
42.8 

7.6 
59.6 
51.6 
21.2 
38.2 
14.9 
29.0 

6.6 
13.1 
48.6 



59.3 
43.6 

9.1 
60.8 
52.7 
21.9 
39.4 
14.0 
29.8 

8.5 
12.7 
49.8 



Special Name 
of Star. 



Spica 

Rigel 

Procyon 

Arcturus 

Betelgeux. . . . 
Aldebaran . . , . 

Sirius 

Fomalhaut. . . 

Antares 

Regulus 

Vega 

Capella 



Declination. 



-10 

- 8 
+ 5 
+19 
+ 7 
+16 
-16 
-30 
-26 
+12 
+38 
+45 



44.4 
17.7 
25.9 
36.0 
23.5 
20.9 
36.4 
3.2 
15.1 
21.6 
42.5 
55.1 



44.6 
17.8 
25.8 
35.9 
23.5 
20.8 
36.6 
3.1 
15.2 
21.5 
42.3 
55.1 



44.6 
17.8 
25.8 
36.0 
23.5 
20.8 
36.6 
2.8 
15.3 
21.6 
42.3 
55.1 



44.6 
17.6 
25.9 
36.1 
23.5 
20.8 
36.4 
2.7 
15.3 
21.6 
42.6 
54.9 



44.5 
17.5 
25.9 
36.0 
23.6 
21.0 
36.3 
2.8 
15.2 
21.5 
42.8 
54.9 



44.7 
17.7 
25.7 
35.7 
23.5 
20.9 
36.5 
2.8 
15.2 
21.3 
42.6 
55.1 



300 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

MERIDIAN TRANSIT OF STARS, 1919 
GREENWICH MEAN TIME OF TRANSIT AT GREENWICH 



Jan. 1 


*Spica 


18h 38' 


Feb. 1 


*Spica 


16h 36' 


1 


*Arcturus 


17h 27' 


1 


*Rigel 


8h 27' 


Mar.l 


*Arcturus 


15h 37' 


1 


*Antares 


17h 49' 


May 1 


*Sirius 


4h 7' 


June 1 


♦Sirius 


2h 6' 


1 


*Canopus 


Ih 46' 


July 1 


*Canopus 


23h 44' 


Dec. 1 


*CapeUa 


12h 32' 



CORRECTIONS TO BE APPLIED TO THE MEAN TIME OF 
TRANSIT ON THE FIRST DAY OF THE MONTH, TO 
FIND THE MEAN TIME OF TRANSIT ON ANY OTHER 
DAY OF THE MONTH. 



Day of 




Month 


Correction 


1 


Oh 0' 


2 


-Oh 4' 


3 


Oh 8' 


4 


Oh 12' 


5 


Oh 16' 


6 


-Oh 20' 


7 


Oh 24' 


8 


Oh 28' 


9 


Oh 31' 


10 


Oh 35' 


11 


-Oh 39' 


12 


Oh 43' 


13 


Oh 47' 


14 


Oh 51' 


15 


Oh 55' 


16 


-Oh 59' 



Day of 




Month 


Correction 


17 


-Ih 3' 


18 


Ih 7' 


19 


Ih 11' 


20 


Ih 15' 


21 


Ih 19' 


22 


Ih 23' 


23 


Ih 27' 


24 


Ih 30' 


25 


Ih 34' 


26 


Ih 38' 


27 


Ih 42' 


28 


lh46' 


29 


Ih 50' 


30 


Ih 54' 


31 


-Ih 58' 



Note: If the quantity taken from this Table is greater than the mean 
time of transit on the first of the month, increase that time by 23h 56' and 
then apply the correction taken from this Table. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 301 



MOON 1919 
DECLINATION 



G.M.T. 
Hrs. 


Decl. 


Diff. 


S. D. 


H.P. 


G.M.T. 
Hrs. 


Decl. 


Diff. S. D. 


H.P. 




February 12 




June 13 


2 


-1-17° 57M 


156 


15'.7 


57'.4 


2 


-21° 36'.2 


12 


14'.9 


54'.6 


4 


17" 4r.5 


160 


15'.6 


57'.3 


4 


21° 35'.0 


16 


14'.9 


54'.6 


6 


17° 25'.5 


163 


15'.6 


5r.3 


6 


21° 33'.4 


21 


14'.9 


54'.7 




February 18 




July 4 


6 


-8° 39'.5 


209 


14'.9 


54'.5 





-5° ^.8M 


216 


15'.0 


55M 


8 


9° 0'.4 


208 


14'.9 


54'.5 


2 


6° 9'.7 


215 


15'.0 


55M 


10 


9° 21'.2 


206 


14'.9 


54'.4 


4 


6° 31'.2 


214 


15'.0 


55'.0 




March 17 




i^.ugust 16 


4 


-6° 52'.8 


215 


14'.9 


54'.5 





-M2° 5'.0 


214 


16M 


59'.2 


6 


7° 14'.3 


212 


14'.9 


54'.5 


2 


12° 26'.4 


211 


16'.2 


59'.2 


8 


7° 35'.5 


212 


14'.9 


54'.5 


4 


12° 47'.5 


208 


16'.2 


59'.2 




April 18 1 




September 14 


4 


-20° 55'.4 


58 


14'.8 


54M 


16 


+19° 42'.3 


93 


16'.3 


59'.6 


6 


21° 1'.2 


53 


14'.8 


54'.2 


18 


19° 51'.6 


88 


16'.3 


59'.6 


8 


21° 6'.5 


50 


14'.8 


54'.2 


20 


20° 0'.4 


82 


16'.3 


59'.6 




April 20 1 




November 25 


10 


-21° 8'.4 


54 


15'.0 


54'.9 


4 


-19° 55'.7 


66 


14'.8 


54'.2 


12 


21° 3'.0 


57 


15'.0 


54'.9 


6 


19° 49M 


70 


14'.8 


54'.2 


14 


20° 57'.3 


62 


15'.0 


55'.0 


8 


19° 42M 


74 


14'.8 


54'.3 




May 20 




December 5 


20 


-13° 6'.5 


193 


15'.4 


56'.4 


10 


18° 25'.4 


127 


16'.7 


6r.2 


22 


12° 47'.2 


195 


15'.4 


56'.5 


12 


18° 38M 


123 


16'.7 


61'.2 




May 21 


14 


18° 50'.4 


117 


16'.7 


61'.3 





-12°27'.7 


199 


15'.4 


56'.6 






2 


12° 7'.8 




15'.5 


56'.6 










201 











302 SIMPLE RULES AND PROBLEMS IN NAVIGATION 









MOON 1919 






TIME OF TRANSIT, MERIDIAN OF GREENWICH 


[ 




Greenwich 






Greenwich 




Date 


Mean Time 


Diff. 


Date 


Mean Time 


DiflP. 


Jan. 9 


6h 4' 


54 


June 15 


13h 55' 


49 


10 


6h 58' 


56 


16 


14h 44' 


48 


11 


7h 54' 




17 


15h 32' 




17 


13h 30' 


46 


July 3 


4h 49' 


44 


18 


14h 16' 


44 


4 


5h 33' 


43 


19 


15h 0' 




5 


6h 16' 




27 


21h r 


53 


7 


7h 45' 


47 


28 


22h 0' 


52 


8 


8h 32' 


48 


29 


22h 52' 




9 


9h 20' 




Feb. 3 


2h 18' 








50 






51 


10 


lOh 10' 




4 


3h 9' 








50 






52 


11 


llh 0' 




6 


4h 1' 








51 






53 


12 


llh 51' 




6 


4h 54' 


56 


18 


16h 43' 


51 


7 


6h 50' 


57 


19 


17h 34' 


54 


8 


6h 47' 




20 


18h 28' 




16 


13h 37' 


43 


Aug. 24 


23h 48' 


46 


17 


14h 20' 


43 


26 


Oh 34' 


46 


18 


15h 3' 




27 


Ih 20' 








43 


Sept. 11 


13h 24' 




19 


15h 46' 








55 


Mar. 4 


Ih 52' 


55 


12 


14h 19' 


56 


5 


2h 47' 


57 


13 


15h 15' 


58 


6 


3h 44' 




14 


16h 13' 




9 


6h 38' 


66 


Oct. 25 


Oh 56' 


47 


10 


71i 34' 


53 


26 


Ih 43' 


48 


11 


8h 27' 




27 


2h 31' 




Apr. 7 


6h 24' 


51 


Dec. 18 


21h 36' 


48 


8 


7h 15' 


48 


19 


22h 24' 


48 


9 


8h 3' 




20 


23h 12' 




May 2 


2h 15' 


62 








3 


3h 17' 


58 








4 


4h 15' 


54 








5 


5h 9' 











SIMPLE RULES AND PROBLEMS IN NAVIGATION 303 



RIGHT ASCENSION AND DECLINATION OF PLANETS 







VENUS 


, 1919 








Greenwich Mean Time 
















Transit 




Apparent Right 




Apparent 




Meridian of 


Date 


Ascension 


Diff. 


Declination 


Diff. 


Greenwich 


Jan. 1 


19h 24' 13" 


325 


—23° 6'. 3 


94 


Oh 44' 


2 


19h 29' 38'i 


324 


22*' 56'. 9 


101 


Oh 45' 


3 


19h 35' 2" 




22"' 46'. 8 




Oh 47' 


23 


21h 19' 19" 


300 


-17° 11'. 6 


226 


Ih 12' 


24 


21h 24' 19" 


298 


■ 16° 49'. 


230 


Ih 13' 


25 


21h 29' 17" 




16° 26'. 




Ih 14' 


28 


21h 44' 5" 


293 


-15° 14'. 1 


248 


Ih 17' 


29 


21h 48' 58" 


292 


14° 49'. 3 


252 


Ih 18' 


30 


21h 53' 50" 




14° 24'. 1 




Ih 19' 


Feb. 7 


22h 32' 6" 


282 


-10° 49'. 6 


282 


Ih 26' 


8 


22h 36'. 48" 


281 


10° 21'. 4 


285 


Ih 27' 


9 


22h 41' 29" 




9° 52'. 9 




Ih 27' 


17 


23h 18' 27" 


273 


- 5° 56'. 8 


304 


Ih 33' 


18 


23h 23' 0" 




5° 26'. 4 




Ih 34' 


Hor. ParaUax Jan. 1, 0'.09; Feb. 1, 


0'.09. 










MARS, 


1919 




Transit 




Apparent Right 




Apparent 




Meridian of 


Date 


Ascension 


Diff. 


Declination 


Diff. 


Greenwich 


Jan. 30 


22h 18' 55" 


179 


-11° 33'. 5 


175 


Ih 44' 


31 


22h 21' 54" 


179 


11° 16'. 


176 


Ih 43' 


Feb. 1 


22h 24' 53" 




10° 58'. 4 




Ih 42' 


June 11 


4h 38' 56" 


178 


+22° 28'. 1 


63 


23h 23' 


12 


4h 41' 54" 


179 


22° 34'. 4 


60 


23h 22' 


13 


4h 44' 53" 




22° 40'. 4 




23h 21' 



Hor. Parallax Feb. 1, 0'.07; June 1, 0'.06 



304 SIMPLE RULES AND PROBLEMS IN NAVIGATION 





JUPITER, 1919 






Greenwich Mean Time 














Transit 


Apparent Right 




Apparent 




Meridian of 


Date Ascension 


Diff. 


Declination 


Diff. 


Greenwich 


Apr. 13 6h 36' 49" 


31 


4-23° 23'. 5 


4 


5h 14' 


14 6h 37' 20" 


33 


23° 23'. 1 


4 


5h 10' 


15 6h 37' 53" 




23" 22'. 7 




5h r 


Dec. 23 9h 21' 11" 


14 


+16'' 17'. 2 


13 


15h 15' 


24 9h 20' 57" 


15 


16° 18'. 5 


14 


15h 10' 


25 9h 20' 42" 




16° 19'. 9 







Hor. Parallax Apr. 1, 0'.03; Dec. 1, 0'.03; Dec. 32, 0'.03 









SATURN, 1919 


















Transit 






Apparent Right 




Apparent 




Meridian of 


Date 




Ascension 


Diff. 


Declination 


Diff. 


Greenwich 


July 


5 


9h 53' 12" 


24 


+14° 18'. 8 


22 


3h 3' 




6 


9h 53' 36" 


25 


14° 16'. 6 


21 


3h 0' 




7 


9h 54' 1" 




14° 14'. 5 




2h 56' 


Oct. 


4 


lOh 35' 20" 


26 


+10° 29'. 3 


24 


21h 44' 




5 


lOh 35' 46" 


25 


10° 26'. 9 


23 


21h 40' 




6 


lOh 36' 11" 




10° 24'. 6 




21h 37' 



Hor. Parallax July 1, O'.Ol; Oct. 1, O'.Ol 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 305 



TABLE 1, P. 107, NAUTICAL ALMANAC 

CORRECTION TO BE APPLIED TO TRUE ALTITUDE OF 

POLARIS 



Local S.T. 


lb 


4b 


7h 


8^ 


9^ 


Om 


— 1° 


6'.7 


-0" 53'.5 


-0° 


8'.7 


+0" 8'.9 


+0° 25'.8 






3 


19 




29 


29 


27 


10m 


1 ° 


7'.0 


0° 51'.6 


0° 


5'.8 


0° ir.8 


0° 28'.5 






2 


19 




30 


29 


27 


20m 


•to 


7'.2 


0" 49'.7 


-0° 


2'.8 


0° 14'.7 


0° 3r.2 






1 


20 




29 


28 


25 


30m 


__1 o 


7'.3 


-0° 47'.7 


+0° 


OM 


+0° 17'.5 


+0° 33'.7 









22 




30 


28 


25 


40m 


1° 


7'.3 


O'' 45'.5 


0° 


3M 


0" 20'.3 


0° 36'.2 






2 


22 




29 


28 


24 


60m 


1 


7M 


0° 43'.3 


0° 


6'.0 


0° 23M 


0° 38'.6 






3 


23 




29 


27 


24 


60m 


__-| o 


6'.8 


-0° 41'.0 


+0° 


8'.9 


+0° 25'.8 


+0° 4r.o 



Local S.T. 


10^1 


11^ 


n^ 


14^ 


15i» 


Om 


+0° 41'.0 


+0° 53'.3 


+1° 6'.7 


+1" 6'.8 


+V 2'.5 




23 


18 


3 


4 


11 


10m 


0° 43'.3 


0° 55M 


1° 7'.0 


r 6'.4 


r r.4 




22 


16 


2 


5 


13 


20m 


0° 45'.5 


0° 56'.7 


r 7'.2 


1° 5'.9 


1° OM 




21 


15 


1 


7 


14 


30m 


+0° 4r.6 


+0° 58'.2 


+ 1'' 7'.3 


+1° 5'.2 


+0° 58'.7 




20 


14 





8 


15 


40m 


0° 49'.6 


0° 59'.6 


r 7'.3 


1" 4'.4 


0° 57'.2 




19 


13 


2 


9 


15 


60m 


0° 51'.5 


1° 0'.9 


1" 7M 


V 3'.5 


0° 55'.7 




18 


12 


3 


10 


17 


60m 


+0° 53'.3 


+1" 2M 


+r 6'.8 


+ 1° 2'.5 


+0° 54'.0 



Local S.T. 


1&^ 


181^ 


2111 


2211 


23^ 


Om 


+0° 54'.0 


+0° 26'.8 


-0° 24'.7 


-0° 40'.2 


-0° 52'.8 




18 


27 


27 


23 


18 


10m 


0° 52'.2 


0° 24M 


0° 27'.4 


0° 42'.5 


0" 54'.6 




19 


27 


27 


23 


17 


20m 


0° 50'.3 


0° 21'.4 


0° 30M 


0° 44'.8 


O'' 56'.3 




20 


28 


26 


21 


16 


30m 


+0° 48'.3 


+0° 18'.6 


-0° 32'.7 


-0° 46'.9 


-0° 57'.9 




21 


29 


26 


21 


14 


40m 


0° 46'.2 


0° lo'.7 


0° 35'.3 


0° 49'.0 


0° 59'.3 




21 


28 


25 


20 


14 


50m 


0° 44M 


0° 12'.9 


0° 37'.8 


0° 51'.0 


1° 0'.7 




23 


29 


24 


18 


12 


COm 


+0° 41'.8 


+0° lO'.O 


-0° 40'.2 


-0° 52'.8 


-V V.9 



ADDENDA 



TO FIND THE DISTANCE OF ANY FIXED POINT BY A 
FOUR-POINT BEARING 

When a lighthouse or any fixed object bears four 
points (or 45°) on the bow, the distance run from the time 
of taking the 4-point bearing until the fixed object is abeam 
(or bears 90°) on the bow, will be the distance off the 
fixed object when abeam, if the vessel has steered the same 
course in the interval. 

Rule: Take a bearing when the fixed object is 4 points 
(or 45°) on the bow. Either read patent log or note time 
by clock. 

When fixed object is abeam (or 90°) on the bow, either 
read patent log or note time by clock. 

If the patent log is used, and it is known that the log is 
accurate, the difference between the first and last reading 
of log will be distance off fixed object when abeam. 
Example: 

Reading of log object bearing 4 points, 28.6 
Reading of log object abeam, 37 . 3 



Distance off object when abeam, 8 . 7 miles 

Note. — It must always be understood that a patent log, 
no matter how accurate, does not keep a correct run of a 
ship, as it does not allow for current, consequently, this 
method cannot absolutely be relied upon. 

When the time by clock is used, and the ship's speed 
over the ground is known, this example is absolutely 
accurate if the bearings have been taken properly. 

Having time of clock at first and second bearing, sub- 
tract less from greater and find number of minutes ship 
has run between bearings. 

Divide the number of minutes by 60, the result will be 
decimal parts of hour. 

Multiply speed of ship over ground by decimal parts of 

307 



308 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

hour, answer will be distance off of fixed object when 
abeam. 

Example: 

PROBLEM NO. 1 

A ship is making 14.8 knots per hour. At 5h 48' A. M. a lighthouse bore 
4 points on the bow and at 6h 23' A. M. was abeam. Required distance 
off Hghthouse when abeam? 

Time abeam 6h 23' 

Time4-points 5h 48' 

Time between brgs, 35' 
60)35 . 00( . 58h Time run between bearings . 58h 

300 Ship's speed over ground 14 . 8 knots 



500 464 

480 232 

58 

20 



8.584 miles off Hghthouse 
when abeam. 

PROBLEM NO. 2 

A ship is steering S 45° E. At 6h 40' P. M. a hght vessel bore South 
and at 7h 29' P. M. bore S 45° W. Ship's speed over ground 14.6 knots 
until 7h 00' P. M. then reduced to 12.3 knots. Required distance 
off light vessel when abeam? 

Time 4-points 6h 40' P. M. Time reducing speed 7h 00' 

Time of reducing speed 7h 00' P. M. Time hght vessel abeam 7h 29' 



Difference 20' at 14.6 knots Difference 29' 

at 12.3 knots 
60)20 . 00( . 33h . 33h difference for first speed 

180 14 . 6 knots first speed 



200 198 
180 132 
33 



20 



4.818 miles distance run on first speed 



60)29 . 00( . 48h . 48h difference for second speed 

240 12 . 3 knots second speed 

500 144 

480 96 



48 



20 



5 . 904 miles distance run on second speed 
4.818 miles distance run on first speed 



10 . 722 miles distance off light vessel when abeam. 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 309 

PROBLEM NO. 3 

A ship is steering N 23° E. Set of current S 54° W. 2^ knots per 
hour. Speed of ship through water 14.3 knots per hour. At 9h 21' P. M. 
a hghthouse bore N 68° E. and at lOh 18' P. M. bore S 67° E. Required 
distance off hghthouse when abeam? 

Time 4-points 9h 21' 14 . 3 knots per hour speed of ship through water 
Time abeam lOh 18' 2.25 knots per hour set of current against or — 



Difference 57' 12.05 knots per hour speed of ship over ground. 

60)57 . 00( . 95h . 95h difference 

540 12.05 knots speed of ship over ground 



300 475 
300 1900 
95 



11 .4475 distance off Hghthouse when abeam. 

PROBLEM NO. 4 

A ship is steering S 35° W. Set of current S 45° W. 2.5 knots per 
hour. Speed of ship through water 12.8 knots per hour. At Ih 14' A. M., 
a lighthouse bore S 80° W and at 2h 12' A. M. bore N 55° W. Required 
distance off hghthouse when abeam? 

Time 4-points Ih 14' 12 . 8 knots per hour speed of ship through water 
Time abeam 2h 12' 2.5 knots per hour set of current fair or plus 



Difference 58' 15.3 knots per hour speed of ship over ground. 

60)58 . 00) . 97h . 97h difference 

540 15.3 knots per hour speed of ship over ground 

400 1071 

420 1377 



14.841 miles distance off hghthouse when abeam 



310 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

DETERMINING SPEED OF SHIP BY PITCH OF WHEEL 
AND NUMBER OF REVOLUTIONS PER MINUTE 

This problem is good for determining the speed of the ship 
by the engine when the pitch of the wheel is known and the 
number of revolutions the propeller is making per minute. 

It must be remembered that it cannot be absolutely 
relied upon to determine the distance a ship has actually 
run or the actual speed of a ship as it does not allow for 
current or head seas or for an}^ other cause that may retard 
or increase the speed of the vessel. 

The difference between the run of a ship by observation 
and the run of a ship by the wheel is called the slip of wheel. 
It is positive if the engine over-runs the ship and negative 
if the ship over-runs the engine. 

Rule: To determine speed of ship by number of revolu- 
tions per minute. 

Multiply number of revolutions per minute by 60, 
result will be number of revolutions per hour. 

Multiply this result by the pitch of the wheel. 

Divide this result by 6080 (the number of feet in a 
nautical mile or knot). 

The answer will be the speed of the ship per hour by 
wheel. 

Example : 

PROBLEM NO. 1 

Pitch of wheel 23 ft.; number of revolutions per minute 71. 
Revolutions 71 
60 

4260 revolutions per hour 
Pitch 23 ft. 



12780 
8520 



6080)97980 . 0(16 . 1 knots per hour speed of ship by engine 

68080 



37180 
36480 



7000 
6080 

920 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 311 



PROBLEM NO. 2 

Ship is steering N 56° W. Current set S E 13^ knots per hour. Pitch 
of wheel 22.4 ft. Revolutions per minute 68.3. Required speed of ship 
per hour by wheel? 

Revolutions 68 . 3 
60 



4098 revolutions per hour 
Pitch 22.4 



16392 
8196 
8196 



6080)91795 . 2(15 . 1 knots per hour speed through water 
6080 1 . 25 set of current against or — 



30995 13 . 85 knots per hour speed over ground 
30400 



5952 
6080 



PROBLEM NO. 3 

Ship is steering S 15° E. Current set S E 1.4 knots per hour. 
Pitch of wheel 21.6 ft. Revolutions per minute 66.8. Required speed 
of ship over ground by wheel? 

Revolutions 66 . 8 
60 



4008 revolutions per hour 
Pitch 21.6 



24048 
4008 
8016 



6080)86572 . 8(14 . 2 knots per hour speed through water 
6080 1 . 4 knots per hour set of current with 

(or plus) 

25772 15.6 knots per hour speed over ground 
24320 



14528 
12160 

2368 



312 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

PROBLEM NO. 4 

Ship is steering S 45° E. Current set N N W 2.2 knots per hour. 
Pitch of wheel 21.3 ft. Revolutions per minute 59.6. Required speed of 
ship through water and over ground? 

Answer. — Speed through water 12.5 knots per hour. 
Speed over ground 10.3 knots per hour. 

PROBLEM NO. 5 

Ship is steering N 16° E. Current set N E 1.9 knots per hour. Pitch 
of wheel 22.1 ft. Revolutions per minute 55.3. Required speed of ship 
through water and over ground by wheel? 

Answer. — Speed of ship through water 12 . 7 knots per hour. 
Speed of ship over ground 14 . 6 knots per hour. 



TO DETERMINE THE PERCENTAGE OF SLIP OF WHEEL 

Rule: With the ship's run by observation and the ship's 
run by wheel, find the difference between them. 

Multiply this difference by 100. 

Divide the result by the largest run. 

Answer will be shp of wheel. 

If the ship's run is larger than the run by wheel, the slip 
will be negative. 

If the run by wheel is larger than the ship's run, the 
slip will be positive. 

Example : 

PROBLEM NO. 1 

A ship runs by observation 300 miles in 24 hours. By wheel, 340 
miles. Required the slip of the wheel? 

Ships run by observation 300 miles 
Ships run by wheel 340 miles 



Difference 40 miles positive. 

100 



340) 4000.0(11.8% positive slip. 
340 

600 
340 

2600 
2720 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 313 



PROBLEM NO. 2 

A ship runs by observation 296 miles in 24 hours. Run by wheel 
290 miles. Required slip of wheel? 

Ship's run by observation 296 miles 
Ship's run by wheel 290 miles 



Difference 6 miles negative. 

100 



296) 600.0(2% negative shp. 
592 

80 

PROBLEM NO. 3 

A ship runs by observation 310 miles in 24 hours. Run by wheel 
336 miles. Required slip of wheel? 

Ship's run by observation 310 miles 
Ship's run by wheel 336 miles 



Difference 26 miles positive. 

100 



336) 2600 . 0(7 . 7% positive slip. 
2352 



2480 
2352 

128 

PROBLEM NO. 4 

A ship runs by observation 402 miles in 24 hours. Run by wheel 
329 miles. Required slip of wheel? 
Answer. — 18. 1% negative slip. 

PROBLEM NO. 5 

A ship runs by observation 415 miles in 24 hours. Run by wheel 
463 miles. Required slip of wheel? 
Answer. — 10.4% positive slip. 

PROBLEM NO. 6 

A ship runs by observation 391 miles in 24 hours. Run by wheel 
389 miles. Required slip of wheel? 
Answer. — 0.5% negative slip. 



314 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



ABSTRACT FROM GENERAL RULES AND REGULATIONS 
OF THE U. S. STEAMBOAT-INSPECTION SERVICE 

The Board of Supervising Inspectors, Steamboat-In- 
spection Service, at a regular annual meeting held in 
Washington, D. C, from January 21 to March 25, 1920, 
entirely revised Rule V of the General Rules and regulations 
for all classes of the Rules, namely: Ocean and Coastwise, 
Great Lakes, Bays, Sounds, and Lakes other than the 
Great Lakes, and Rivers, which revised Rule V in full for 
the various classes as follows: 

OCEAN AND COASTWISE 

Rule V. — Licensed Officers 

Original License 

1 . Before an original license is issued to any person to act as a master, 
mate, pilot, or engineer, he shaU personally appear before some local 
board or supervising inspector for examination. Any person who has 
attained the age of 19 years and has had the necessary experience shall 
be eligible for examination; Provided, that no person shaU receive 
a license as master, first mate, second mate, chief engineer, first assistant 
engineer, or second assistant engineer, before reaching the age of 21 
years. 

Inspectors shall, before granting an original license to any person 
to act as an officer of a vessel, require the apphcant to make written 
appUcation upon the blank form furnished by the Department of Com- 
merce, to be filed in the inspector's office. When practicable, apphcants 
for masters', mates', pilots', or engineers' license shall present to the 
inspectors, to be filed with their appHcations, discharges or letters 
from the master or other officer under whom they have served, certify- 
ing to the name of the vessel and in what capacity the applicant has 
served under him; also period of such service. Inspectors shall also, 
when practicable, require apphcant for pilot's license to have the written 
indorsement of the master and engineer of the vessel upon which he has 
served, and of one licensed pilot, as to his qualifications. In the case of 
apphcants for original engineer's license, they shall also, when practicable, 
have the endorsement of the master and engineer of the vessel on which 
they have served, together with one other hcensed engineer. 

The first hcense issued to any person by a United States Inspector 
shall be considered an original Hcense, where the United States record 
show no previous issue to such apphcant. 

No original license shall be issued to any naturalized citizen on less 
experience in any grade than would have been required of a citizen of 
the United States by birth. (Sec. 4405, R. S.) 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 315 



Visual Examinations Requiked for Original and Renewed 

Licenses 

2. No original license as master, mate, or pilot of any vessel shall be 
issued except upon the official certificate of a surgeon of the Public 
Health Service respecting the vision of the person applying for such 
original hcense. The word ''original" as contemplated in this section 
shall mean the first Hcense of any character issued to a master, mate, 
or pilot, and shall not be held to mean, for instance, that a license issued 
to a master who was previously licensed as a mate or pilot shall be 
considered an original master's license. 

No hcense as master, mate, or pilot of any class of vessel shall be 
renewed except upon the official certificate of a surgeon of the Public 
Health Service that the color sense of the applicant for renewal is 
normal. 

Where an appHcant for renewal of license is situated so that it would 
put him to great inconvenience or expense to appear before a surgeon of 
the Public Health Service for examination, the certificate of a reputable 
physician or oculist as to the color sense of the applicant shall be accepted 
in lieu of the certificate of the surgeon of the Public Health Service. 

In case an applicant for original license or renewal of Hcense is pro- 
nounced color-blind, he may, in the discretion of the inspectors, be 
limited to act as master, mate, or pilot on a vessel navigating in daylight 
only. 

Nothing herein contained shall debar an applicant who has lost the 
sight of one eye from securing the renewal of his license, providing that 
his color sense is normal. (Sees. 4439, 4440, 4442, R. S.) 

Examinations 

3. No original master's, mate's, pilot's, or engineer's license shall 
be issued hereafter or grade increased except upon written examination 
by a Board of Local Inspectors or a Supervising Inspector, which written 
examination shaU be placed on file in the office of the inspectors issuing 
said license: Provided, However, That upon navigable waters of the 
United States newly opened to steamboat navigation, and where the 
only pilots obtainable are illiterate Indians or other natives, the fact 
that such persons can neither read nor write shall not be considered a 
bar to such Indians or other natives receiving license as pilot of steam 
vessels, provided they are otherwise qualified therefor. 

Before granting or renewing a license inspectors shall satisfy them- 
selves that the applicants can properly hear the bell and whistle signals. 

When any person makes application for Hcense it shall be the duty 
of the Local Inspectors to give the applicant the required examination 
as soon as practicable. (Sees. 4405, 4439, 4440, 4441, 4442, R. S.) 

Reexaminations and Refusals of Licenses 

4. Any applicant for license who has been duly examined and refused 
may come before the same local board for reexamination at anj^ time 
thereafter, but he shall not be examined by any other local board until 
one year has expired from the date of the refusal. 

If the inspectors shall decHne to grant the applicant the Hcense 



316 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

asked for, they shall furnish him a statement, in writing, setting forth 
the cause of their refusal to grant the same. (Sees. 4405, 4455, R. S.) 

Pkeparation of Licenses 

5. All licenses hereafter issued to masters, mates, pilots, and engineers 
shall be filled out on the face with pen and black ink instead of type- 
written. Inspectors are directed, when licenses are completed, to 
draw a broad pen and black-ink mark through all unused spaces in 
the body thereof, so as to prevent, as far as possible, illegal interpolation 
after issue. 

Every person receiving license or certificate of lost license shall sign 
same upon back thereof immediately upon its receipt. (Sec. 4405, R. S.) 

Certificate of Lost License 

6. In case of loss of license of any class from any cause, the Inspectors, 
upon receiving satisfactory evidence of such loss, shall issue a certificate 
to the owner thereof, which shall have the authority of the lost license 
for the unexpired term, unless in the mean time the holder thereof shall 
have the grade of his license raised, after due examination, in which case 
a Hcense in due form for such grade may be issued. (Sec. 4405, R. S.) 

Parting with License 

7. Any license granted to a master, mate, pilot, engineer, or operator 
shall be immediately revoked, if, for any purpose, the holder thereof 
voluntarily parts with its possession or places it beyond his personal 
control by pledging or depositing it with another. (Sec. 4405, R. S.) 

Renewal of License 

8. Whenever an officer shall apply for a renewal of his license for 
the same grade, the presentation of the old license, with satisfactory 
certificate of visual examination, where required, and with oath of office, 
shall be considered sufficient evidence of his title to renewal, which old 
license and oath of office shall be retained by the Inspectors upon their 
official files as the evidence upon which the Hcense was renewed; Provided, 
That it is presented within 12 months after the date of its expiration, 
unless such title has been forfeited or facts shall have come to the 
knowledge of the Inspectors which would render a renewal improper; 
nor shall any license be renewed more than 30 days in advance of the 
date of the expiration thereof, unless there are extraordinary circum- 
stances that shall justify a renewal beforehand, in which case the reasons 
therefor must appear in detail upon the records of the inspectors renewing 
the license. 

Whenever an officer shall apply for renewal of his hcense for same 
after 12 months after the date of its expiration, he shall be required to 
pass an examination for the same grade of license. The renewed hcense 
in either case shall receive the next higher number for number of issue 
of present grade and for number of issues of all grades. 

Whenever a Ucensed officer makes application for a renewal of his 
license, he shall appear in person before some_board of local inspectors 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 317 

or supervising inspector, except that upon renewal of such hcense for 
the same grade, when the distance from any local board or supervising 
inspector is such as to put the person holding the same to great incon- 
venience and expense to appear in person, he may, upon taking oath 
of office before any person authorized to administer oaths, and forwarding 
the same, together with the license to be renewed and certificate of visual 
examination where required, to the local board or supervising inspector of 
the district in which he resides or is employed, have the same renewed by 
the said inspectors, if no vafid reason to the contrary be known to them; 
and they shall attach such oath to the stub end of the license, which is 
to be retained on file in their office; Provided, However, That any officer 
holding a license, and who is engaged in a service which necessitates 
his continuous absence from the United States, may make appHcation 
in writing for renewal and transmit the same to the board of local 
inspectors, with his certificate of citizenship, if naturalized, and a state- 
ment of the appficant, verified before a consul or other officer of the 
United States authorized to administer an oath, setting forth the reasons 
for not appearing in person; and upon receiving the same the board 
of local inspectors that originally issued such license shall renew the same 
and shall notify the applicant of such renewal, and no license as master, 
mate, or pilot of any class of vessel shall be renewed without furnishing 
a satisfactory certificate of color-bHndness. (Sees. 4405, 4438, R. S.) 

Extension of Route and Raise of Grade of Licenses 

9. Licensed officers serving under five years' license, entitled by 
license and service to raise of grade, after passing examination, shall 
have issued to them new Hcenses for the grade for which they are 
qualified, the local inspectors to ffie in their offices the old Hcense when 
surrendered, with the report of the circumstances of the case, but the 
grade of no license shall be raised, except as hereinafter provided, unless 
the applicant can show one year's actual experience in the capacity for 
which he has been licensed. 

Inspectors shall, before granting an extension of route or raise of 
grade of license, require the applicant to make his written application 
upon the blank form of application for extension of route or raise of 
grade of license furnished by the Department. When practicable, 
applicants for extension of route or raise of grade of license shall present 
to the inspectors, to be filed with the application, discharges or letters 
from the master or other officer under whom they have served, or other 
satisfactory documentary evidence, certifying to the name of the vessel 
and in what capacity the applicant has served; also period of such 
service. 

If any board of local inspectors is satisfied by the documentary 
evidence submitted that a pilot is entitled by experience and knowledge 
to unhmited tonnage it may remove any tonnage restrictions which may 
have been placed upon his license by any other board of local inspectors. 

Except as hereinafter provided, practical service in the deck depart- 
ment of an ocean or coastwise vessel propelled by machinery shaU be 
accepted when offered in documentary evidence by any person appljdng 
for an original license or raise of grade as equal to the same amount 
of service in any ocean or coastwise steam passenger vessel. 

Service on the United States Lighthouse Tenders propelled by 



318 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

machinery shall be considered as equivalent experience for raise of 
grade as that obtained on vessels subject to inspection by this Service. 
Service on United States Light vessels propelled by machinery shall 
be considered as one-haK experience for raise of grade as that obtained 
on vessels subject to inspection by this Service. (Sec. 4405, R. S.) 

Examination foe Renewal of Master's or Pilot's License 

10. It shall be the duty of all inspectors, before renewing an existing 
license, to a master or pilot of steam vessels, for any waters, who has 
not been employed as master or pilot on such waters during the three 
years preceding the application for renewal, to satisfy themselves, by 
an examination in writing, or orally, to be taken down in writing by the 
inspectors, that such officers are thoroughly famiUar with the pilot 
rules upon the waters for which they are Hcensed. (Sees. 4439, 4442, 
R. S.) 

Laws, General Rules and Regulations, and Pilot Rules to be 
Furnished Licensed Officers 

11. Every master, mate, pilot, and engineer of vessels shall, when 
receiving an original Hcense, a renewed license, or a raise of license, 
be furnished by the inspectors with a copy of the Laws Governing 
the Steamboat-Inspection Service, and a copy of the General Rules and 
Regulations Prescribed by the Board of Supervising Inspectors, and 
every master and pilot of vessels and operator of motor vessels shall, 
when receiving an original license, a renewed license, or a raise of grade 
of license, be furnished by the inspectors with a pamphlet copy of the 
rules and regulations governing pilots and other statutes upon which 
such rules are founded, applicable to the waters on which their Ucenses 
are intended to be used, as stated in the body thereof. (Sec. 4405, 
R. S.) 

Suspension and Revocation of Licenses 

12. When the license of any master, mate, pilot, or engineer is 
revoked such Hcense expires with such revocation, and any hcense sub- 
sequently granted to such person shall be considered in the hght of an 
original hcense except as to number of issue. And upon the revocation 
or suspension of the license of any such officer said license shall be sur- 
rendered to the local inspectors or supervising inspector ordering such 
suspension or revocation. 

When the license of any master, mate, engineer, or pilot is suspended 
the inspectors making such suspension shall determine the term of its 
duration, except that such suspension shall not extend beyond the time 
for which the license was issued. 

The suspension or revocation of a joint license shall debar the person 
holding the same from the exercise of any of the privileges therein 
granted, so long as such suspension or revocation shall remain in force. 
(Sec. 4450, R. S.) 

Misconduct of Licensed Officers 

13. Whenever a supervising, local, or assistant inspector of steam 
vessels, or any of them, shall find on board any vessel subject to the 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 319 

provisions of Title LII of the Revised Statutes any licensed officer under 
the influence of liquor or other stimulants to such an extent as to unfit 
him for duty, or when any hcensed officer shall use abusive or insulting 
language to any inspector or assaults any such inspector while on official 
duty, the local inspectors or the supervising inspector shall immediately 
suspend or revoke the hcense of the officer so offending without further 
trial or investigation. 

The fact of a licensed officer being under the influence of liquor in 
the presence of the inspector or inspectors to such an extent as to unfit 
him for duty while on board a vessel shall be sufficient cause for such 
suspension or revocation. (Sees. 4405, 4450, R. S.) 

Licenses to Officers of Vessels Owned by the United States 

14. Any person who has served at least one year as master, com- 
mander, pilot, or engineer of any steam vessel owned and operated by 
the United States in any service in which a license as master, mate, 
pilot, or engineer was not required at the time of such service shall be 
entitled to Hcense as master, mate, pilot, or engineer, if the inspectors 
upon written examination, as required for applicants for original license, 
may find him quahfied: Provided, That the experience of any such 
apphcant within three years of making appfication has been such as to 
qualify him to serve in the capacity for which he makes application 
to be licensed. (Sees. 4439, 4440, 4441, 4442, R. S.) 

Reports of Accidents to Vessels 

15. The licensed officer in command of any vessel subject to the 
inspection of the Steamboat-Inspection Service shall report in writing 
and in person to the board of local inspectors nearest the port of first 
arrival any accident to said vessel involving loss of life, or damage to 
property to an approximate amount exceeding $100, and shaU also 
report in the same manner any casualty or loss of life from whatever 
cause of any person on board such vessel. If the accident happens upon 
the high seas or without the jurisdiction of inland waters, the board 
to whom the report is first made shall make the investigation, but if the 
accident occurred within the jurisdiction of inland waters, the report 
shall be transmitted to the board within whose jurisdiction the accident 
occurred, which board shall make the investigation except in cases 
where, in the judgment of the Supervising Inspector General, better 
results may be obtained by another board conducting the investigation, 
in which case the Supervising Inspector General is authorized to direct 
such investigation by another board : Provided, That when from distance 
it may be inconvenient to report in person it may be done in writing 
only, and the report sworn to before any person authorized to admin- 
ister oaths. 

Whenever a vessel subject to the inspection of the Steamboat- 
Inspection Service colHdes with fight ship, buoy, or other aid to 
na\4gation under the jurisdiction of the Bureau of Lighthouses, or is 
connected with any such colhsion, it shall be the duty of the licensed 
officer in command of such vessel to report the accident to the nearest 
board of local inspectors. When any coUision of this character is 
reported to a board of local inspectors, those officers shall immediately 



320 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

transmit such information to the Lighthouse Inspector of the District 
in which the coUision occurs. (Sees. 4405, 4448, R. S.) 

Only Certain Persons Allowed in Pilot House and on Navigator's 

Bridge 

16. Masters and pilots of steamers carrying passengers shaU exclude 
from the Pilot houses and Navigator's Bridge of such steamers, while 
underway, all persons not connected with the navigation of such steamers, 
except officers of the Steamboat-Inspection Service, Coast Guard, and 
engineer officers of the United States Army in charge of the improve- 
ment of that particular waterway, when upon business: Provided, That 
licensed officers of steamboats, persons regularly engaged in learning 
the profession of pilot, officers of the United States Navy, United States 
Coast and Geodetic Survey, and Lighthouse Service, assistant engineers 
of the Engineer Department of the United States Army connected with 
the improvement of that particular waterway, and the engineer officers 
connected with the construction and operation of the Panama Canal 
may be allowed in the Pilot house or upon the Navigator's Bridge upon 
the responsibility of the officer in charge. 

The master of every such passenger and ferry steamer shaU keep 
three printed copies of this section of Rule V posted in conspicuous 
places on such steamer, one of which shall be kept in the Pilot house. 

Such printed copies shall be furnished by the Department of Com- 
merce to Local Inspectors for distribution. (Sec. 4405, R. S.) 

Station Bills, Drills, and Reports of Masters 

17. It shall be the duty of the officer in charge of every steamer 
carrjdng passengers and all other vessels of over 500 gross tons, pro- 
pelled by machinery and subject to inspection, to cause to be prepared 
a station bill for his own department, and one also for the engineer's 
department, in which shall be assigned a post or station of duty for every 
person employed on board such vessel in case of fire or other disaster, 
which station biUs shall be placed in the most conspicuous places on 
board for the observation of the crew. And it shall be the duty of such 
master, or of the mate or officer next in command, once at least in each 
week to call all hands to quarters and exercise them in discipline, and 
in the unlashing and swinging out of the life boats, weather permitting, 
and in the use of the fire pumps, and all other appai^atus for the safety 
of life on board of such vessel, with especial regard for the drill of 
the crew in the method of adjusting life preservers and educating passen- 
gers and others in this procedure and to see that all the equipments 
required by law are in complete working order for immediate use; and 
the fact of the exercise of the crew, as herein contemplated, shall be 
entered upon the vessel's log book, stating the day of the month and hour 
when so exercised; and it shall be the duty of the inspectors to require 
the officers and crew of all such vessels to perform the aforesaid drills 
and discipline in the presence of the said inspectors at intervals suffi- 
ciently frequent to assure the said inspectors by actual observation 
that the foregoing requirements of this section are complied with; the 
master of every passsenger steamer shall also report monthly to the 
local inspectors the day and date of such exercise and drill, the condition 
of the vessel and her equipment, and also the number of passengers 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 321 

carried, and any neglect or omission on the part of the officer in com- 
mand of such vessel to strictly enforce this rule shall be deemed cause 
for the suspension or revocation of the Ucense of such officer. 

The General fire-alarm signal shall be a continuous rapid ringing 
of the ship's bell for a period of not less than 20 seconds, and this signal 
shall not be used for any other purpose whatsoever. The master of 
any vessel may establish such other emergency signals in addition to 
the ringing of the ship's bell, as will provide that all the officers and all 
the crew of the steamer will have positive and certain notice of the 
existing emergency. 

Three copies of this section shall be furnished every steamer carrying 
passengers, and one copy to all other vessels to which this section applies 
to be framed under glass and posted in conspicuous places about the 
vessel. (Sec. 4405, R. S.) 

Vessels Requiring Licensed Masters 

18. There shall be a duly licensed master on board every steam 
vessel of more than 150 gross tons whenever such steamer is under way, 
and also upon every ocean and coastwise sea-going merchant vessel of 
the United States propelled by machinery, and upon every ocean-going 
vessel carrjdng passengers, subject to the Inspection Laws of the United 
States. (Sees. 4439, 4463, R. S.) 

Substituting Service in Next Lower Grade for Raise of Grade 

19. Except as hereinafter provided, an applicant who has served in 
a lower grade than that for which he is Hcensed may substitute service 
in the grade next below that for which he is licensed, which service shall 
count one-half in computing experience for raise of grade. For example, 
if an applicant holds chief mate's hcense and has served nine months as 
chief mate and six months as second mate, the six months service as 
second mate shall count as three months as chief mate in computing 
experience. (Sec. 4405, R. S.) 

Master of Ocean Steam Vessels 

20. An applicant for license as master of ocean steam vessels shall 
be eligible for examination after he has furnished satisfactory docu- 
mentary evidence to the Local Inspectors that he has had the following 
experience : 

First. One year's service as chief mate of ocean steam vessels, or. 
Second. One year's service as chief mate of coastwise steam vessels of 

1000 gross tons or over, or. 
Third. Two years' service as second mate of ocean steam vessels, one 

year of such service while holding a hcense as chief mate of ocean 

steam vessels, or. 
Fourth. Five years' service as third mate of ocean steam vessels, two 

years of such service while holding a Hcense as chief mate of 

ocean steam vessels, or, 
Fifth. Five years' service on ocean or coastwise sail vessels of 200 gross 

tons or over, two years of said service as master of such sail 

vessels while holding a license as master of sail vessels, for license 

as master of freight or towing vessels, or, 



322 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

Sixth. Six months' service as master of coastwise steam vessels of 100 
gross tons or over, or, 

Seventh. Thirty-six months' service as master of steam vessels of 4000 
gross tons, or over, upon the waters of the Great Lakes, together 
with 12 months' service as chief or second mate of ocean or coast- 
wise steam vessels. (Sec. 4439, R. S.) 

Examination for Master of Ocean Steam Vessels 

21. An applicant for license as master of ocean steam vessels shall 
pass a satisfactory examination as to his knowledge of the following 
subjects: 

1. Latitude by meridian altitude of the sun. 

2. Latitude by exmeridian altitude of the sun. 

3. Latitude by meridian altitude of a star. 

4. Latitude by pole star. 

5. Longitude by chronometer. (A. M. or P. M.) 

6. Position by Sumner's method. 

7. Ship's position by dead reckoning. 

8. Mercator sailing. 

9. Deviation of the compass by an amplitude. 

10. Deviation of the compass by an azimuth. 

11. Time of high water at a given point. 

12. Chart navigation. 

13. Storm signals. 

14. International code of signals. 

15. International rules for preventing collisions at sea. 

16. Use of gun and rocket apparatus for saving life from ship wreck, as 

practised by the United States Coast Guard. 

17. Such further examination of a non-mathematical character as the 

local inspectors may require. (Sec. 4439, R. S.) 

Master of Coastwise Steam Vessels 

22. An applicant for hcense as master of coastwise steam vessels 
shall be eligible for examination after he has furnished satisfactory 
documentary evidence to the local inspectors that he has had the follow- 
ing experience : 

First. One year's service as chief mate of ocean or coastwise steam 
vessels, or. 

Second. Two years' service as second mate of ocean or coastwise steam 
vessels, one year of such service while holding a license as chief 
mate of ocean or coastwise vessels, or, 

Third. Five years' service as third mate of ocean or coastwise steam 
vessels, two years of such service while holding a Hcense as chief 
mate of ocean or coastwise steam vessels, or. 

Fourth. Two years' service as master of lake, bay, or sound steam 
vessels of 500 gross tons or over, and, in addition thereto, one 
year's service as officer in charge of a watch on ocean or coast- 
wise steam vessels while holding a license as master of lake, bay, 
or sound steam vessels, or. 

Fifth. Five years' service on ocean or coastwise sail vessels of 200 gross 
tons or over, two years of which service shall have been as master 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 323 

of such sail vessels for license as master of coastwise freight or 

towing vessels, or, 
Sixth. One year's service as a licensed master of ocean or coastwise 

sail vessels of 700 gross tons or over, for a license as master of 

coastwise freight or towing vessels, or, 
Seventh. Two years' service as master or first-class pilot of lake, bay, 

or sound towing steamers of 150 gross tons or over, for a license 

as master of coastwise towing steam vessels of 750 gross tons 

or under, or. 
Eighth. Two years' service as master of steam vessels of 2500 gross tons 

or over, on the Great Lakes, and other lakes, bays, and sounds, or, 
Ninth. Two years' service as a licensed master of steam vessels of 250 

gross tons or over, engaged in the ocean or coastwise fisheries, 

for Hcense as master of coastwise freight or towing vessels. 

(Sec. 4439, R. S.) 

Examination for Master of Coastwise Steam Vessels 

23. An appHcant for license as master of coastwise steam vessels 
on routes exceeding 300 miles shall pass a satisfactory examination as 
to his knowledge of the following subjects: 

1. Longitude by chronometer. 

2. Latitude by meridian altitude of the sun. 

3. Latitude by pole star. 

4. Ship's position by dead reckoning. 

5. Azimuth of sun by tables. 

6. Determination of distance from a fixed object. 

7. Chart navigation. 

8. International rules for preventing collisions at sea. 

9. Storm signals. 

10. Use of gun and rocket apparatus for saving life from shipwreck as 

practised by the United States Coast Guard. 

11. Such further examination of a non-mathematical character as the 

local inspectors may require. 
An applicant for hcense as master of coastwise steam vessels on 
routes not exceeding 300 miles shall pass a satisfactory examination as 
to his knowledge of the following subjects: 

1. Chart navigation. 

2. Aids to navigation on route. 

3. Determination of distance from a fixed object. 

4. International rules for preventing colhsions at sea. 

5. Storm signals. 

6. Such further examination of a non-mathematical character as the 

local inspectors may require. (Sec. 4439, R. S.) 

Masters of Sail Vessels 

24. An apphcant for license as master of sail vessels of over 700 gross 
tons shall be eligible for examination after he has furnished satisfactory 
documentary evidence to the Local Inspectors that he has had the follow- 
ing experience: 

First. Five years' service in the deck department of sail vessels of 200 



324 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

gross tons or over; one year of such service shall have been as master 

of sail vessels of 500 gross tons or over; or, 
Second. Two years' service as master of sail vessels of two nundred gross 

tons or over; or, 
Third. Two years' service as mate of sail vessels of 500 gross tons or over; 

or, 
I'ourth. Two years' service as master of auxiliary sail vessels of 100 
gross tons or over. (Sec. 4439, R. S.) 

Examination foe Licenses as Master of Sail Vessels 

25. An applicant for license as master of sail vessels shall pass a 
satisfactory examination as to this knowledge of the following subjects: 

1. Latitude by meridian altitude of the sun. 

2. Latitude by pole star. 

3. Longitude by chronometer (A. M. or P. M.). 

4. Ship's position by dead reckoning. 

5. Mercator sailing. 

6. Deviation of the compass by an amplitude. 

7. Deviation of the compass by an azimuth. 

8. Chart navigation. 

9. International code of signals. 

10. Storm signals. 

11. International rules for preventing collisions at sea. 

12. Use of gun and rocket apparatus for saving life from shipwreck, as 

practised by the United States Coast Guard. 

13. Such further examination of a non-mathematical character as the 

local inspectors may require. (Sec. 4439, R. S.) 

Chief Mate of Ocean Steam Vessels 

26. Any apphcant for license as chief mate of ocean steam vessels 
shall be eligible for examination after he has furnished satisfactory 
documentary evidence to the local inspectors that he has had the follow- 
ing experience: 

First. One year's service as second mate of ocean steam vessels; or, 

Second. One year's service as second mate of coastwise steam vessels 
of 1000 gross tons or over; or. 

Third. Two years' service as officer in charge of a watch on ocean or 
coastwise steam vessels, while holding aUcense as second mate 
of ocean or coastwise steam vessels; or, 

Fourth. Two years' service as master of lake, bay, or sound steam 
vessels of 1000 gross tons or over, together with six months' 
service as officer in charge of a watch on ocean or coastwise steam 
vessels of 1000 gross tons or over; or. 

Fifth. Five years' service in the deck department of ocean or coastwise 
sail vessels of 200 gross tons or over; t¥/o years of such service 
shall have been as chief mate of such ocean or coastwise sail vessels, 
for license as chief mate of ocean freight or towing steam vessels; 

Sixth. One year's service as a hcensed master of steam vessels of 250 
gross tons or over, engaged in the ocean or coastwise fisheries, 
for license as ehief mate of ocean freight or towing steam vessels; 
or, 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 325 

Seventh. Five years' experience in the deck department of any ocean or 
coastwise sail vessel of 100 gross tons or over; two years of such 
service shall have been as master of such vessels for Hcense as 
chief mate of ocean freight or towing steam vessels. (Sec. 4440, 
R. S.) 

Second Mate of Ocean Steam Vessels 

27. Any applicant for license as second mate of ocean steam vessels 
shall be ehgible for examination after he has furnished satisfactory 
documentary evidence to the local inspectors that he has had the follow- 
ing experience : 

First. One year's service as third mate of ocean or coastwise steam 
vessels; or, 

Second. Four years' service in the deck department of ocean or coastwise 
steam vessels ; one year of such service shall have been as quarter- 
master and one year as quartermaster or boatswain of such steam 
vessels; or. 

Third. A graduate who has served two years in the seamanship class 
of a State Nautical Schoolship and completed two ocean or coast- 
wise cruises before graduation, together with six months' service 
in the deck department of ocean or coastwise steam or sail vessels 
of 200 gross tons or over; Provided, That where the graduate 
has completed the two cruises, but not the two years' service 
required, additional service equal to the difference of time shall 
be served on vessels of the class required for the probationary 
period of six months; or. 

Fourth. Three years' service in the deck department of ocean or coast- 
wise sail vessels of 200 gross tons or over; one year of such service 
shall have been as second mate of such vessel; or. 

Fifth. Nine months' service as quartermaster and nine months' service 
as quartermaster or boatswain on ocean or coastwise steam 
vessels, a total of 18 months' service, while holding a license as 
third mate of ocean or coastwise steam vessels; or. 

Sixth. Two years' service in the deck department of any ocean or coast- 
wise sail vessel of 100 gross tons or over, together with one year's 
service in the deck department of ocean or coastwise steam vessels, 
for Ucense as second mate of ocean or coastwise steam vessels 
of 750 gross tons or under; or. 

Seventh. One year's service as master or first-class pilot, of lake, ba3^ 
or sound steam vessels of 500 gross tons or over, together with 
six months' service in the deck department of ocean or coastwise 
steam vessels of 1000 gross tons or over, while holding a license 
as a master or first-class pilot. (Sec. 4440, R. S.) 

Examination for License as Chief Mate and Second Mate of 
Ocean Steam Vessels 

28. An applicant for Hcense as chief mate or second mate of ocean 
steam vessels shall be required to pass a satisfactory examination as to 
his knowledge of the following subjects: 

1. Latitude by meridian altitude of the sun. 

2. Latitude by meridian altitude of a star. 



326 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

3. Longitude by chronometer (A. M. or P. M.). 

4. Speed of ship by propeller revolutions. (Note: For chief mate only.) 

5. Deviation of the compass by an azimuth. 

6. Ship's position by dead reckoning. 

7. Mercator's saiHng. 

8. Determination of distance from a fixed object. 

9. Chart navigation. 

10. Storm signals. 

11. International code of signals. 

12. International rules for preventing coUisions at sea. 

13. Stowage of cargo. 

14. Use of gun and rocket apparatus for saving life from shipwreck, as 

practised by the United States Coast Guard. 

15. Such further examination of a non-mathematical character as the 

local inspectors mav require. CSec. 4440, R, S.) 

Third Mate of Ocean Steam Vessels 

29. Any appHcant for Hcense as third mate of ocean steam vessels 
shall be ehgible for examination after he has furnished satisfactory 
documentary evidence to the local inspectors that he has had the follow- 
ing experience : 
First. Two years' service in the deck department of ocean or coastwise 

steam vessels; or, 
Second. A graduate of the seamanship class of a State Nautical School- 
ship who shall have made two ocean or coastwise cruises during 
his period of training; or, 
Third. Three years' service in the deck department of ocean or coast- 
wise sail vessels of 100 gross tons or over. Service on such sail 
vessels engaged in the ocean or coastwise fisheries shall be accepted 
as meeting the requirements of this paragraph; or, 
Fourth. One year's service as master or pilot of lake, bay, or sound 
steam vessels of 150 gross tons or over, together with six months' 
service in the deck department of ocean or coastwise steam 
vessels; or, 
Fifth. Three years' service in the deck department of ocean or coastwise 
steam or sail vessels of less than 100 gross tons, together with one 
year's service in the deck department of ocean or coastwise steam 
vessels; or, 
Sixth. Three years' service in the deck department of lake, bay, or 
sound steam vessels, together with one year's service in the deck 
department of ocean or coastwise steam vessels; or. 
Seventh. Twenty-four months' service as a hcensed first-class pilot 
of steam vessels of 4000 gross tons or over on the Great Lakes 
and other lakes, bays, or sounds; or. 
Eighth. Three years' service in the deck department of steam vessels 
of 100 gross tons or over, engaged in the ocean or coastwise 
fisheries. 
Ninth. Any person who has attained the age of 19 years and who has 
graduated from a regular estabhshed high school or college, may, 
upon recommendation of the master or masters under whom he 
has served, be examined for third mate of ocean or coastwise 
steamers after having served not less than 15 months in the 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 327 

deck department of ocean or coastwise steamers of 2000 gross 
tons or over. 
Tenth. Any person who has completed the intensive training course 
subscribed by the United States Navy, and who has been com- 
missioned as ensign in the United States Naval Reserve Force, may, 
upon the recommendation of the master or masters or the Naval 
officers or officers under whom he has served, be examined for third 
mate of ocean or coastwise steamers, after having actually served not 
less than four months at sea, after being commissioned as officer 
of the watch or as extra watch officer in company with the officer 
in charge of the bridge. (Sec. 4440, R. S.) " 

Examination for License as Third Mate of Ocean Steam Vessels 

30. An applicant for license as third mate of ocean steam vessels 
shall be required to pass a satisfactory examination as to his knowledge 
of the following subjects: 

1. Latitude by meridian altitude of the sun. 

2. Deviation of the compass by an azimuth of the sun. 

3. Longitude by chronometer (A. M. or P. M.). 

4. Ship's position by dead reckoning. 

5. Mercator's sailing. 

6. Determination of distance from a fixed object. 

7. Chart navigation. 

8. International rules for preventing collisions at sea. 

9. Stowage of cargo. 

10. Storm signals. 

11. Such further examination of a non-mathematical character as the 

local inspectors may require. (See 4440, R. S.) 

Chief Mate of Coastwise Steam Vessels 

31. An applicant for license as chief mate of coastwise steam vessels 
shall be ehgible for examination after he has furnished satisfactory 
documentary evidence to the local inspectors that he has had the follow- 
ing experience: 

First. One year's service as second mate of ocean or coastwise steam 
vessels; or. 

Second. Two years' service as officer in charge of a watch on ocean or 
coastwise steam vessels, one year of such service while holding a 
Ucense as second mate of ocean or coastwise steam vessels; or. 

Third. One year's service as master or first-class pilot of lake, bay, or 
sound steam vessels of 150 gross tons or over, together with one 
year's service as quartermaster or wheelsman on ocean or coast- 
wise steam vessels while holding a license as such master or first- 
class pilot; or, 

Fourth. Two years' service as master or first-class pilot of lake, bay, or 
sound towing vessels for license as chief mate of coastwise towing 
vessels of 750 gross tons or under; or. 

Fifth. Three years' service in the deck department of ocean or coast- 
wise steam vessels for license as chief mate of coastwise steam 
vessels of 750 gross tons or under; or. 

Sixth. One year's service as a licensed master or two years' service a^ a 



828 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

licensed mate on ocean or coastwise steam vessels of 250 gross 
tons or over, engaged in the ocean or coastwise fisheries for hcense 
as chief mate of freight or towing steamers; or, 

Seventh. Five years' ser^dce in the deck department of any ocean or 
coastwise sail vessel of 100 gross tons or over, two years of such 
service shall have been as master of such vessel, for Hcense as 
chief mate of freight or towing steam vessels; or, 

Eighth. Two years' service in the deck department of ocean or coast- 
wise sail vessels together with one year's ser^dce in the deck 
department of ocean or coastwise steam vessels, for hcense as 
chief mate of coastwise steam vessels of 750 gross tons or under 
(Sec. 4440, R. S.) 



Second Mate of Coastwise Stea^i Vessels 

32. An applicant for hcense as second mate of coastwise steam 
vessels shall be eligible for examination after he has furnished satis- 
factory documentary evidence to the local inspectors that he has had 
the following experience: 

First. One year's ser^dce as third mate of ocean or coast\\dse steam 
vessels; or. 

Second. One year and six months' ser\dce in the deck department of 
ocean or coastmse steam vessels, nine months of which ser\dce 
shall have been as quartermaster or boatswain, a total of 18 
months' service, while holding a license as third mate of such vessels 
or, 

Third. Four years' service in the deck department of ocean or coast- 
wise steam vessels, one year of such service to have been as 
quartermaster or boatswain of such steam vessels ; or, 

Fourth. Two years' ser\dce in the deck department of any ocean or coast- 
wise sail vessel of 100 gross tons or over, together -^dth one years' 
service in the deck department of ocean or coastwise steam 
vessels, for a license as second mate of coastwise steam vessels 
of 750 gross tons or under; or, 

Fifth. A graduate who has serv^ed two years in the seamanship class 
of a State Nautical Schoolship and completed two ocean or 
coastwise cruises before graduation, together \^dth six months' 
service in the deck department of ocean or coastwise steam or sail 
vessels: Provided, That where the graduate has completed the 
two cruises, but not the two years' service required, additional 
service equal to the difference in time shall be served on ocean 
or coastwise steam or sail vessels; or. 

Sixth. One year's service as a licensed master or first-class pilot of lake, 
bay, or sound steam vessels of 150 gross tons or over, together 
■with six months' sendee in the deck department of ocean or 
coastwise steam vessels; or, 

Seventh. One year's service as a Hcensea mate on ocean or coastwise 
vessels of 150 gross tons or over, engaged in the fisheries (Sec. 
4440, R. S.). 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 329 

Examination fok License as Chief Mate and Second Mate of 
Coastwise Steam Vessels 

33. An applicant for license as chief mate or second mate of coast- 
wise steam vessels on routes exceeding 600 miles shall be required to 
pass a satisfactory examination as to his knowledge of the following 
subjects: 

1. Latitude by meridian altitude of the sun. 

2. Ship's position by dead reckoning. 

3. Determination of distance from a fixed object. 

4. International rules for preventing collisions at sea. 

5. Chart navigation. 

6. Stowage of cargo. 

7. Storm signals. 

8. Such further examination of a non-mathematical character as the 
local inspectors may require. 

An applicant for license as chief mate or second mate of coastwise 
steam vessels on routes of 600 miles or less shall be required to pass a 
satisfactory examination as to his knowledge of the following subjects: 

1. Chart navigation. 

2. Aids to navigation on route. 

3. Determination of distance from a fixed object. 

4. Marking of a lead line. 

5. International rules for preventing collisions at sea. 

6. Storm signals. 

7. Such further examination of a non-mathematical character as the 

local inspectors may require. (Sec. 4440, R. S.) 

Third Mate of Coastwise Steam Vessels 

34. An applicant for license as third mate of coastwise steam vessels 
shall be eligible for examination after he has furnished satisfactory 
documentary evidence to the local inspectors that he has had the follow- 
ing experience: 

First. Two years' service in the deck department of ocean or coastwise 
steam vessels. 

Second. A graduate of the seamanship class of a State Nautical School- 
ship who shall have made two ocean or coastwise cruises during 
his period of training; or, 

Third. Three years' service in the deck department of ocean or coast- 
wise sail vessels of 100 gross tons or over. Service on such sail 
vessels engaged in the ocean or coastwise fisheries shall be acceoted 
as meeting the requirements of this paragraph; or, 

Fourth. One year's service as master or pilot of lake, bay, or souna, or 
river steam vessels of 150 gross tons or over, together wdth six 
months' service in the deck department of ocean or coastwise 
steam vessels; or. 

Fifth. Twenty-four months' service as a licensed first-class pilot of 
steam vessels of 2500 gross tons or over, on the Great Lakes, and 
other lakes, bays, or sounds; or. 

Sixth. Three years' service in the deck department of ocean or coast- 
wise steam or sail vessels of less than 100 gross tons, together 



330 SIMPLE RULES AND PROBLEMS IN NAVIGATION 

with one year's service in the deck department of ocean or coast- 
wise steam vessels; or, 

Seventh. Three years' service in the deck department of lake, bay, or 
sound steam vessels, together with one year's service in the deck 
department of ocean or coastwise steam vessels; or, 

Eighth. Three years' ser\T[ce in the deck department of steam vessels 
of 100 gross tons or over, engaged in the ocean or coastwise fish- 
eries. 

Ninth. Any person who has attained the age of 19 years and who has 
graduated from a regular established high school or college may 
upon the recommendation of the master or masters under whom 
he has served, be examined for third mate of ocean or coastwise 
steamers after having served not less than 15 months in the deck 
department of ocean or coastwise steamers of 200 gross tons or over. 

Tenth. Any person who has completed the intensive training course 
prescribed by the United States Navj'', and who has been com- 
missioned ensign in the United States Naval Reserve Force may, 
upon the recommendation of the master or masters or the naval 
officer or officers under whom he has served, be examined for 
third mate of ocean or coastwise steamers after having actually 
served not less than four months at sea, after being commissioned, 
as officer of the watch or as extra watch officer in company with 
the officer in charge of the bridge. (Sec. 4440, R. S.) 

Examination for License as Third Mate of Coastwise Steam 

Vessels 

35. An applicant for license as third mate of coastwise steam vessels 
shall pass a satisfactory examination as to his knowledge of the follow- 
ing subjects: 

1. Chart navigation. 

2. Determination of distance from a fixed object. 

3. International rules for preventing collisions at sea. 

4. Marking lead line. 

5. Storm signals. 

6. Such further examination of a non-mathematical character as the 

local inspectors may require. (Sec. 4440, R. S.) 

Indorsement of Master's or Mate's License as Pilot 

36. Whenever a master or mate desires to act in the double capacity 
of master and pilot, or mate and pilot, and furnishes the necessary 
evidence of his qualifications, the local inspectors shall indorse such 
pilot routes on the certificate of license. (Sec. 4443, R. S.) 

License of Owner as Master of Steam Yacht 

37. Whenever the owner of a steam or sailing yacht of over 100 gross 
tons, who has reached the age of 21 years, and who has had three years' 
experience in sailing such vessels, applies for a license authorizing him 
to act as master of steam yachts for coastwise and ocean navigation, 
the local inspectors shall examine the apphcant as to his knowledge of 
the rules of the road, fog signals, signal fights (inland and international;) 
the use of the lead and line; the use of the patent and chip logs, the 



SIMPLE RULES AND PROBLEMS IN NAVIGATION 331 

compass, variation and deviation of the compass, the use of the drag, 
the use of oil during storms, bell signals between pilot house and engine- 
room, handling of steam vessels, laws of storms, course and distance 
by chart, keeping the log book, middle latitude saihng, Mercator's 
saihng method of obtaining latitude and longitude by dead reckoning, 
latitude by altitude of either the sun, moon, or stars; longitude by 
chronometer (time sights). Practical problems shall be given in the 
subjects of latitude and longitude, examination shall be in writing, 
which shall be kept on file in the office of the local inspectors. If said 
examination is satisfactory to the local inspectors, they shall issue to the 
applicant a master's hcense, authorizing him to discharge the duties 
of master of steam yachts, either for coastwise or ocean navigation. 
(Sees. 4439, 4442, R. S.) 

Master, Mate, and Pilot of Steam Pilot, Fishing, Porto Rican, 
AND Hawaiian Vessels 

38. Any applicant for original license to act as master of steam 
pilot boats, or of steamers navigating the waters of the whaling grounds 
in the Alaskan seas, or of steamers engaged exclusively in the business 
of whale fishing, or of steamers engaged in the Atlantic, Pacific, or Gulf 
Coast fisheries, or of steam or sail vessels navigating between ports of 
the Hawaiian Islands, or between ports of the island of Porto Rico, 
shall have had at least three years' experience in the deck department 
of such vessels, and except as hereinafter provided, for an original license 
as mate the applicant shall have had two years' experience in the deck 
department of such vessels, which fact shall be verified by documentary 
evidence; and such applicant shall only be subjected to such examination 
as shall satisfy the inspectors that the applicant is capable of navigating 
such vessels. It is Provided, That any person who has had at least 
five years' experience on sail vessels licensed in the fisheries of the United 
States, two years of which have been as master or mate of such sailing 
vessels, may be examined for license as master or mate of steam fishing 
vessels to be employed exclusively in the Atlantic, Pacific, and Gulf 
Coast fisheries. The license issued under this section shall state in the 
body thereof (for Coastwise only) Pacific or Atlantic Coast, as the case 
may be, and between what ports on either of said coast. 

It is Further Provided, That any applicant for original license who has 
had three years' experience in the deck department on steam pilot boats, 
or who has had two years' experience in the deck department on steam 
pilot boats and one year's experience on sail pilot boats shall be eligible 
for examination for license as mate of steam pilot boats. 

It is Further Provided, That said master's or mate's license may be 
endorsed as pilot on such inland waters on the above-named coasts 
as the local inspectors at the various ports may find the holder qualified 
to act on as pilot, after examination by the local inspectors, such exami- 
nation to be in writing and preserved in the files of the inspectors' office. 
(Sees. 4439, 4440, 4442, R. S.) 



ANSWERS TO PROBLEMS 
for THE YEAR 1921 

Supplement to 

SIMPLE RULES AND PROBLEMS 

IN NAVIGATION 



BY 

CHARLES H. CUGLE 



NEW YORK 
E. P. DUTTON AND COMPANY 

681 Fifth Avenue 



Copyright 1921, by 
E. P. DUTTON & COMPANY 



All Rights Reserved 



Printed in the United States of America 



ANSWERS TO PROBLEMS FOR THE 
YEAR 1921 



LATITUDE BY MERIDIAN ALTITUDE OF SUN 



Prob. No. 1. Ans. Lat. 27° 53' 19" North 






' 2. " 


" 5° 31' 29" South 






' 3. " 


" 0° 29' 30" South 






i 4. " 


" 25° 42' 14" North 






' 5. " 


" 25° 31' 53" North 






' 6. " 


" 32° 42' 31" North 






c 7_ M 


" 48° 34' 41" North 






' 8. " 


" 35° 20' 31" South 






' 9. " 


'' 42° 27' 30" North 






' 10. " 


' 59° 25' 47" North 






' 11. " 


' 12° 26' 14" South 






' 12. " 


' 40° 55' 05" North 






' 13. " 


' 56° 03' 03" North 






' 14. " 


' 34° 38' 15" North 






' 15. " 


' 23° 30' 32" South 






' 16. " 


' 47° 07' 11" South 






' 17. " 


• 0° 12' 05" South 



LATITUDE CONSTANT 



Prob. No. 18. 
" 19. 
" 20. 
" 21. 



^ns. Lat. 40° 59' 11" North 
" " 43° 12' 01" North 
" '* 30° 46' 14" South 
" " 9° 36' 25" South 



4 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



TIME OF STAR'S MERIDIAN PASSAGE 



^OB 


. No. 


1. 


Mer. Pas. Jan. 10th 18h 01m 


( ( 


< ( 


2. 


" Feb. 16th 16h 26m 


( ( 


( ( 


3. 


" June 3rd Ih 36m 


<( 


(( 


4. 


'' May 12th 3h 23m 



LATITUDE BY MERIDIAN ALTITUDE OF STAR 



Prob. No. 



1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 
10. 
11. 
12. 



Ans. Lat. 



*Rigel 55° 02' 44' 


North 


*Procyon 18° 11' 08' 


North 


*Arcturus 34° 17' 25' 


South 


*Spica 30° 03' 22' 


North 


*Betelgeux 2° 31' 48' 


South 


*Aldebaran 68° 12' 25' 


North 


*Sirius 32° 14' 44' 


North 


*Fomalhaut41°48'42' 


North 


*Antares 38° 03' 57' 


South 


*Foinalhautl3'34'41' 


South 


*Regulus 52° 10' 23' 


North 


*Sirius 37° 00' 47' 


North 



LONGITUDE BY SUN 



PaoB. No. 1. Ans. Long. 93° 52' 45" West 






• 2. 


' 91° 25' 45" West 






' 3. " 


' 75° 39' 45" East 






* 4. " 


' 88° 42' 00" East 






' 5. " 


' 76° 29' 00" West 






' 6. " ' 


' 59° 33' 15" West 






' 7. " ' 


' 28° 47' 30" East 






' 8. " 


' 94° 44' 30" West 






' 9. " 


' 137° 35' 15" West 






' 10. '' 


* 86° 54' 15" East 



ANSWERS TO PROBLEMS FOR THE YEAR 1921 



NOON POSITION SIGHTS 



RO 


B. No. L Ans. Lat. at sight 50° 37' 36" N Long. 166° 42' 45"E 






* noon 50° 16' 24" N 


( < 


165° 53' 45" E 


(( 


" 2. ** 


' sight 26° 22' 29" N 


( ( 


91 ° 48' 45" W 






' noon 25° 31' 17" N 


( ( 


92° 16' 45" W 


11 


" 3. *' 


' sight 36° 59' 00" S 


it 


23°19'45"E 






' noon 37° 21' 36" S 


it 


22° 51' 45" E 


(( 


" 4. " 


' sight 21° 55' 34" S 


<< 


103° 33' 30" W 






' noon 22° 35' 48" S 


tt 


103° 19' 30" W 


(( 


" 5. '* 


' sight 17° 24' 48" N 


tt 


156° 32' 30" E 






' noon 18° 16' 00" N 


ft 


157° 01' 00" E 


(( 


" 6. ** 


' sight 28° 42' 40" N 


tt 


7° 14' 00" W 






' noon 28° 16' 28" N 


tt 


8° 31' 00" W 


(( 


,, 7 i« 


' sight 28° 17' 42" S 


tt 


124° 52' 45" E 






' noon 27° 23' 00" S 


tt 


125° 25' 45" E 


(( 


" 8. " 


' sight 0°04'56"N 


1 1 


0°07'30"W 






' noon 0°10'30"N 


(« 


0°22'54"E 


(1 


a 9. ^* 


' sight 22° 23' 48" S 


tt 


103° 25' 15" E 






' noon 23° 15' 00" S 


1 1 


103° 50' 15" E 


it 


1' 10. *' 


' sight 41° 22' 36" N 


tt 


166° 36' 15" W 






* noon 41* 16' GO" N 


tt 


167° 59' 15" W 



DEVIATION OF AZIMUTH OF SUN 



Prob. No. 1. Error of Compass 6° 52' W Deviation 12° 52' W 

ti 2. " " " 5°40'E " 35°20'W 

ti » 3^ ti u tt goQO'W " 16°00'W 

tt tt 4 it u tt o°00' " 6°00'W 



6 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



DEVIATION BY AMPLITUDE 



Prob. No. 1. Ans. Error of Compass 33° 05' E Dev. 25° C5' East 




2. ' 


( << ( 




3°23'W ' 


' 21° 37' East 




3. ' 


( (< < 




22°31'E ' 


' 16° 31' East 




4. ' 


( << < 




1°53'E ' 


' 13° 07' West 




5. ' 


( « < 




iroo'w ' 


' 9° 00' West 




6. * 


( <( ( 




25M4'E ' 


' 4° 46' West 




7. ' 


( << ' 




15° 47' E ' 


' 18° 47' East 




8. ' 


( (< < 




34° 50' E ' 


' 44° 50' East 




9. ' 


< <( ( 




6°43'W ' 


* 3° 17' East 




10. ' 


( << ( 




11°42'W ' 


' 14° 42' West 




11. ' 


( (< ( 




24° 42' E ' 


' 10° 18' West 


tt t 


, 12. ' 


( (< ( 




9°58'W ' 


' 12° 58' West 



LATITUDE BY POLARIS 



Prob. No. 1. 

' " 2. 

' '* 3. 

" " 4. 

" " 5. 

'* " 6. 

" " 8. 

• " 9. 

• " 10. 
" *• 11. 

* *' 12. 

* *' 13. 
It it 14. 



Ans. Latitude 25 
28 



50' 20" N 
22' 03" N 
27° 16' 21" N 
36° 23' 33" N 
27° 02' 53" N 
22° 29' 15" N 
42° 53' 37" N 
60° 46' 03" N 
49° 17' 27" N 
30° 36' 13" N 
47° 31' 42" N 
27° 28' 25" N 
25° 18' 46" N 
13° 25' 41" N 



ANSWERS TO PROBLEMS FOR THE YEAR 1921 



ALTITUDE AZIMUTH, LONGITUDE BY SUN AND MERCATOR'S 
SAILING COMBINED 

Prob. No. 1. Ana. Lat. at eight 12*' 39' 22" N. Long. 86^ 20' 00" W 
Lat. at noon 12" 25' 22" N. Long. 87° 06' 30" W 
Error of compass 14° 21' E. Dev. 30° 21' E 
True courses 62° 57' W. Distance 2595 miles. 

" 2. Ans. Lat. at sight 28°44' 24" S. Long. 61° 14' 00" E 
Lat. at noon 28° 17' 00" S. Long. 60° 28' 00" E 
Error of compass 9° 28' E. Dev. 23° 28' E 
True course N 73 ° 58' W. Distance 2625 miles. 

** " 3. Ans. Lat. at sight 5° or 42" N. Long. 150° 59' 15" W 
Lat. at noon 4° 16' 00" N. Long. 151° 14' 15" W 
Error of compass 17° 41' W. Dev. 10° 19' E 
True course S 80° 39' W. Distance 3595 miles. 

" "4. Ans. Lat. at sight 22° 03' 17" N. Long. 24° 22' 15" E 
Lat. at noon 22° 41' 17" N. Long. 23° 43' 45" E 
Error of compass 1° 03' W. Dev. 20° 03' W 
True course S 45° 42' W. Distance 1982 miles. 

•* ** 6. Ans. Lat. at sight 35° 54' 15" S. Long. 29° 43' 00" E 
Lat. at noon 36° 16' 51" S. Long. 29° 15' 00" E 
Error of compass 33° 55' W. Dev. 28° 55" W 
True course N 40° 52' W. Distance 2971 miles. 

** V 6. Ans. Lat. at sight 3° 05' 13" N. Long. 0° 17' 30" W 
Lat. at noon 3° 11' 07" N. Long. 0° 13' 00" E 
Error of compass 41 ° 48' E. Dev. 16° 48' E 
True course N 69° 01' W. Distance 3538 miles. 



8 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



LATITUDE BY MERIDIAN ALTITUDE OF PLANET 

P^OB. No. 1. Ans. Latitude by Planet "Saturn" 55° 49' 13" N 

" " 2. " " '' " ''Jupiter" 54° 13' 34" S 

" " 3. " " '• " "Venus" 35° 44' 05" S 

" " 4. " " " " "Jupiter" 30° 21' 48" N 



LATITUDE BY EX-MERIDIAN ALTITUDE OF SUN 



Prob. No. 1. Ans. Lat. 43° 16' 07" N 




' 2. " 


' 37° 17' 06" S 




' 3. " 


' 47° 56' 45" S 




• 4. 


' 22° 43' 13" S 




' 5. " 


' 40° 59' 03" N 




' 6. " 


* 39° 08' 15" N 




' 7. 


' 48° 23' 03" S 




' 8. '' 


' 46° 57' 49" N 




* 9. " 


' 47° 47' 12" N 




' 10. " 


' 33° 28' 37" N 




' 11. •' 


' 13° 15' 53" N 




' 12. " 


' 32° 22' 56" N 




' 13. " 


' 24° 44' 48" S 




'14. 


' 46° 57' 22" S 



LONGITUDE BY FIXED STAR 



Prob. No. 1. 


Ans. 


Long, by *Spica 


94° 22' 00" W 




* " 2. 




" *Vega 


90° 64' 80" W 




' " 3. 




' ' *Regulus 


110° 00' 45" E 




" 4. 




' ' * Antares 


166° 29' 45" W 




" 5. 




*CapeUa 


33° 33' 00" W 




* " 6. 




' ' *Aldebaran 


0° 07' 00" E 




' " 7. 




*CapeUa 


5° 14' 00" W 




' " 8. 




* ' *Spica 


113° 11' 30" W 




' " 9. 




" *Betelgeux 


164° 50' 30" W 




" 10. 




♦Rigel 


7° 41' 45" E 



ANSWERS TO PROBLEMS FOR THE YEAR 1921 9 



LONGITUDE BY PLANET 

Prob. No. 1. Ans. Long, by Planet "Mars" 34° 38' 00" W 

" 2. " " " "Saturn" 54° 56' 30" W 



LATITUDE BY MERIDUN ALTITUDE OF MOON 



Prob. No. 1. 


Ans. L 


at. 68° 08' 26" N 


" " 2. 




" 3° 10' 08" S 


" ** 3. 




" 83° 30' 15" N 


i< a 4 




'' 9° 05' 59" S 


'' '' 6. 




" 38° 52' 17" S 


''. tt 6. 




" 1°32'39"S 



TIME OF MOON'S MERIDIAN PASSAGE 



Prob. No. 1. 


Ans. Mer. Pas. Jan. 28d 4h Im A. M. 


" 2. 


" " " Feb. 7d Oh 14m P.M. 


" '' 3. 


" '' " Mar. lOd Ih 2m P.M. 


" 4. 


" " " Apr. 8d Oh 6m P. M. 


" 5. 


" " *' June 16d 9h 27m P. M. 


" 6. 


" " '' July lid 5h 9m P.M. 



LONGITUDE AT SUNRISE AND SUNSET OBSERVATIONS 

Prob. No. 1. Ans. Long. 95° 50' 15" E 
ti a 2. '' '' 96° 38' 45" W 



PHI PRIME SIGHT FOR LATITUDE 

Prob. No. 1. Ans. Lat. 9° 22' 48" S 
a 2. " '' 26° 49' 58" S 
a 3^ ci << 50° 13' 24" N 



10 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



SUMNER'S METHOD 

Peob. No. 1. 1st Line of Bearing: Lat. 40" N Long. 45° 12' 15" W 

" 41" N " 44" 04' 30" W 

2d Line of Bearing: " 40" N " 46" 55' 30" W 

" 41"N " 44" 56' 45" W 



MARCQ ST. HILAIRE METHOD 



Prob. No. 1. 1st Line of Bearing: Sun: Alt. Diff. -2' 15' 



2d Line of Bearing 
2. 1st Line, *Siriu8, W. 



4. 



5. 



2d 

1st 
2d 
3d 

1st 
2d 
3d 

4th 

1st 
2d 



6. 1st 
2d 



♦Capella, W. 

*Polaris 
*Vega, E. 
♦Capella, W. 

♦Capella, W. 
*Vega, E. 
*Spica, E. 
*Procyon, W. 

Sun 
Sun 

*Regulus, W. 
*Arcturus, E. 



" " +7' 48" 

" " - 2' 30" 
" " -14' 13" 

Lat. 40" 34' 28" N 
Alt. Diff. - 5' 45" 

- 0'07" 

+ 1'50" 
+ 4' 15" 

- 2' 05" 

- 2' 20" 

-42' 14" 
-38' 46" 

+ 1'39" 
-17' 20" 



ANSWERS TO PROBLEMS FOR THE YEAR 1921 11 



TIME OF HIGH AND LOW WATER 



ROB. No. 1. 


High Wa 
Low ' 


iter Jan. 
' Jan. 


18d 2h 47m A. M. 

ISd 8h 56m A. M. 


3h 13m P. M 
9h 22m P. M 


" 2. 


High ' 
Low ' 


' Jul. 
' Jul. 


19d 8h 09m A. M. 
19d 2h 14m A. M. 


8h 32m P. M 
2h 37m P. M 


" 3. 


High ' 
Low ' 


' Sep. 
' Sep. 


13d 4h 25m A. M. 
13d lOh 39m A. M. 


4h 48m P. M 
llh 02m P. M 


" 4. 


High ' 
Low ' 


' Feb. 
' Feb. 


17d 4h 29m A. M. 
17d lOh 47m A. M. 


4h 58m P. M. 
llh 16m P. M 


" 5. 


High ' 
Low ' 


' Aug. 
' Aug. 


26d lOh 58m A. M. 
26d 4h 46m A. M. 


llh 25m P. M. 
5h 13m P. M 


" 6. 


High ' 
Low * 


' Jul. 
' Jul. 


8d lOh 34m A. M. 
8d 3h 55m A. M. 


llh 03m P. M 
4h 24m P. M 


" 7. 


High ' 
Low ' 


' Dec. 
' Dec. 


19d 9h 17m A. M. 
19d 3h 07m A.M. 


9h 44m P. M. 
3h 34m P. M 


" 8. 


High ' 
Low ' 


' Feb. 
' Feb. 


4d 8h 49m A. M. 
4d 2h 53m A. M. 


9h 12m P. M 
3h 16m P. M 


" " 9. 


High ' 
Low ' 


' May 
' May 


4d 2h 09m A. M. 
4d 7h 24m A. M. 


2h 32m P. M 
7h 47m P. M 


"10. 


High ' 
Low ' 


' Jan. 
' Jan. 


lOd 5h 17m A.M. 
lOd llh 34m A. M. 


5h 40m P. M. 
llh 57m P. M. 


"11. 


High ' 
Low ' 


' Mar. 
' Mar. 


5d 12h 02m A. M. 
5d 6h 09m A. M. 


12h 25m P. M 
6h 32m P. M. 


" "12. 


High ' 
Low ' 


' Oct. 
' Oct. 


26d 2h 34m A. M. 
26d 8h 55m A. M. 


3h 00m P. M. 
9h 21m P. M. 



12 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



EXAMPLES FOR PRACTICE 



LATITUDE BY MERIDIAN ALTITUDE OF SUN 



Pros. No. 1. 
u " 2. 
" " 3. 

" " 5. 
" " 6. 



Lat. 17° 00' 57" N 
23° 25' 59" S 
' 30° 16' 26" N 
34° 21' 34" S 
24° 08' 17" N 
14° 55' 18" S 



LATITUDE BY MERIDIAN ALTITUDE OF STAR 



PROB. No. 1. 

2. 
3. 

4. 
5. 
6. 



Lat 



by *Spica 
*Arcturus 
♦Aldebaran 
*Aiitares 
*Regiilus 



38° 12' 14" N 
42° 14' 20" S 
73° 42' 43" N 
35° 07' 55" S 
45° 30' 32" S 



♦Formalhaut 16° 47' 05" N 



TIME OF STAR'S MERIDIAN PASSAGE 



ROB. No 


1. Mer. Pas. *Spica 


Jan. 16d 5h 41m A. M. 




2. " 


" *Rigel 


Feb. 12d 7h 42m P. M. 




3. " 


' ' *Antares Mar. 20d 4h 36m A. M. 




4. " 


' ' *Sirius 


May 19d 2h 55m P. M. 




5. '' 


' ' *Canopii3 June 7d Ih 20m P. M. 


-- 


6. '' 


" *CapeUa Dec. 6d 12h 14m A. M. 
LONGITUDE BY SUN 




Prob. 


No. 1. Long. 


80° 21' 00" W 




<< 


" 2. 


120° 16' 00" E 




^^ 


" 3. " 


124° 16' 30" W 




it 


" 4. " 


.35° 18' 00" W 




<« 


*' 5. " 


38° 20' 45" E 




till 


" 6. " 


122° 34' 30" W 



ANSWERS TO PROBLEMS FOR THE YEAR 1921 13 



NOON POSITION SIGHTS 



Prob. No. 1. 



2. 



4. 



5. 



6. 



At Sight: Lat. 28° 56' 36" N Long. 46° 08' 15" W 


At Noon: 


' 28° 16' 00" N 


' 46° 32' 45" W 


At Sight: 


' 13° 54' 06" S 


' 98° 55' 15" E 


At Noon: 


' 14° 18' 00" S 


' 99° 25' 45" E 


At Sight: 


" 41° 54' 54" N 


' 92° 11' 15" W 


At Noon: 


'' 41° 10' 00" N 


' 91° 33' 15" W 


At Sight: 


' 36° 15' 54" S 


' 24° 14' 00" E 


At Noon: 


" 36° 42' 00" S 


' 24° 50' 00^' E 


At Sight: 


' 31° 54' 54" N 


' 109° 59' 15" W 


At Noon: 


' 31° 15' 00" N 


' 110° 18' 15" W 


At Sight: 


' 32° 23' 12" N 


* 27° 34' 00" E 


At Noon: 


' 31° 48' 00" N 


' 28° 09' 00" E 



DEVIATION BY AZIMUTH OF SUN 



Pbob. No. 1. 


Error of Compass 6° 10' W 


Dev. 1° 50' E 


" 2. 


15° 00' E 


" 7° 00' E 


" 3. 


5°11'E 


" 11°11'E 


u 4 


5° 25' E 


" 2°35'W 


" 6. 


7° 38' W 


" 0° 24' E 


" " 6. 


1° 24' W 


" 5° 24' W 



DEVIATION BY AMPLITUDE OF SUN 



ROB. No. 1. 


Error of Compass 7° 25' W 


Dev 


1°35'E 


" " 2. 


9°00'E 




5° 00' E 


" " 3. 


13°30'E 




3° 30' E 


" 4. 


" " 8°42'E 




1°18'W 


" " 6. 


4°53'W 




6° 53' W 


'' " 6. 


l''22'W 




5° 38' E 



14 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



LATITUDE BY POLARIS 



Prob. No. 1. 


Lat. 16" 66' 30" N 


" " 2. 


" 24" 15' 50" N 


" " 3. 


" 29" 01' 47" N 


" " 4. 


" 15" 17' 40" N 


" " 5. 


" 37" 27' 28" N 


" " 6. 


" 40" 57' 19" N 



ALTITUDE AZIMUTH, LONGITUDE BY SUN AND MERCATOR'S 
SAILING COMBINED 



Prob. No. 1. At Sight: Lat. 33" 00' 06" N. Long. 47° 29' lo" E 
At Noon: " 33" 32' 18" N. " 47° 45' 45" E 
Error of Compass 6" 59' W. Dev. 7" 59' W 
True Course N 21" 49' W. Distance 945.7 miles. 

*' " 2. At Sight: Lat. 36" 09' 12" N. Long. 126" 25' 15" W 
At Noon: " 35" 59' 00" N. " 126" 54' 45" W 
Error of Compass 38" 39' E. Deviation 16° 24' E 
True Course S 66" 20' E. Distance 1517 miles. 

ti " 3. At Sight: Lat. 47" 50' 42" N. Long. 22" 46' 00" E 
At Noon: " 47" 25' 00" N. " 22" 00' 00" E 
Error of Compass 5" 41' W. Dev. 10" 11' W 
True course S 23" 8' W. Distance 1452 miles. 

?• f 4. At Sight: Lat. 38" 40' 00" S. Long. 105" 1' 45" W 
At Noon: " 38" 20' 00" S. " 105" 1' 45" W 
Error of Compass 38" 41' W. Dev. 3" 41' W 
True Course N 67" 56' W. Distance 4504 miles. 

** " 6. At Sight: Lat. 15" 26' 00" S. Long. 56° 12' 00" E 
At Noon: tt 16" 00' 00" S. " 66° 37' 45" E 
Error of Compass 15" 47' E. Dev. 2° 43' W 
True course N 67" 52' W. Distance 3859 miles. 

!* " 6. At Sight: Lat. 50" 35' 36" S. Long. 68" 37' 15" W 
At Noon: '' 50" 02' 00" S. " 68" 09' 30" W 
Error of Compass 10" 26' W. Dev. 3" 52' E 
True Course N 50" 02' E. Distance 2338 miles. 



ANSWERS TO PROBLEMS FOR THE YEAR 1921 15 



LATITUDE BY MERIDIAN ALTITUDE OF PLANET 

Prob. No. 1. Lat. by Planet "Mars" 18° 41' 33" S 

" " 2. " " "Saturn" 45" 38' 28'' S 

" 3. " " "Venus" 44° 48' 20" N 

'* " 4. " " "Jupiter" 41° 11' 69" N 



LATITUDE BY EX-MERIDIAN ALTITUDE OF SUN 



Prob. No. 1. 


Lat. 24° 16' 18" N 


" M 2. 


" 17° 21' 15" S 


" *' 3. 


" 53° 25' 27" N 


a a 4 


" 24° 43' 36" S 


'* " 5. 


" 48° 51' 52" S 


'' *' 6. 


" 1°26'39"N 



LONGITUDE BY FIXED STAR AND PLANET 



Prob. No. 1. 
" 2. 



Long. *Sirius 60° 9' 45" E 
' ' *Arcturus 141 ° 24' 00" W 

3. " *Procyon 41° 6' 45" W 

4. " *Spica 64° 56' 45" E 

5. Planet "Venus" 29° 35' 00" W 

6. " "Saturn" 91° 44' 00" E 



LATITUDE BY MERIDIAN ALTITUDE OF MOON 



Prob. No. 1. Lat. 57° 37' 44" S 



" " 2. 


" 27° 37' 10" N 


** " 3. 


" 19° 11' 24" S 


*' " 4. 


" 33° 16' 51" N 


" " 5. 


" 25° 39' 18" S 


*' " 6. 


" 12° 21' 50" N 



16 SIMPLE RULES AND PROBLEMS IN NAVIGATION 



LONGITUDE BY SUNRISE AND SUNSET 



Prob. No. 1. 


Long. 19'' 25' 45" W 


" " 2. 


7" 40' 45" E 


" " 3. 


" 98° 16' 00" W 


" " 4. 


" 78° 35' 30" E 


*' '' 5. 


" 65° 00' 00" E 


" " 6. 


" 125° 56' 15" E 



TIME OF HIGH AND LOW WATER 



Prob. No. 1. High Water Jan. 28d 8h 02m A. M. 



Low 



Jan. 28d Ih 49m A. M. 



(( < < 


2. 


High 
Low 


(I 


Jul. 
Jul. 


4d lOh 15m A. M. 
4d 4h 11m A. M. 


(( 1 1 


3. 


High 
Low 


1 1 


Mar. 
Mar. 


9d 9h 02m A. M. 
9d 2h 50m A. M. 


t( ( ( 


4. 


High 
Low 


ft 
it 


Sep. 
Sep. 


12d 4h 23m A. M. 
12d lOh 34m A. M. 


55 1* 


5. 


High 

Low 


55 


Jim. 
Jun. 


led 4h 56m A.M. 
16d lOh 59m A. M. 


( ( (( 


6. 


High 
Low 


It 


May- 
May 


3d 3h 47m A. M. 
3d 9h57mA. M. 



8h 27m P. M. 
2h 14m P. M. 

lOh 45m P. M. 
4h 41m P. M. 

9h 25m P. M. 
3h 13m P. M. 

4h 46m P. M. 
lOh 57m P. M. 

lOh 59m A. M. 
llh 23m P. M. 

4h 09m P. M. 
lOh 19m P. M. 



